How can anything ever fall into a black hole as seen from an outside observer?

It is true that, from an outside perspective, nothing can ever pass the event horizon. I will attempt to describe the situation as best I can, to the best of my knowledge.

First, let's imagine a classical black hole. By "classical" I mean a black-hole solution to Einstein's equations, which we imagine not to emit Hawking radiation (for now). Such an object would persist for ever. Let's imagine throwing a clock into it. We will stand a long way from the black hole and watch the clock fall in.

What we notice as the clock approaches the event horizon is that it slows down compared to our clock. In fact its hands will asymptotically approach a certain time, which we might as well call 12:00. The light from the clock will also slow down, becoming red-shifted quite rapidly towards the radio end of the spectrum. Because of this red shift, and because we can only ever see photons emitted by the clock before it struck twelve, it will rapidly become very hard to detect. Eventually it will get to the point where we'd have to wait billions of years in between photons. Nevertheless, as you say, it is always possible in principle to detect the clock, because it never passes the event horizon.

I had the opportunity to chat to a cosmologist about this subject a few months ago, and what he said was that this red-shifting towards undetectability happens very quickly. (I believe the "no hair theorem" provides the justification for this.) He also said that the black-hole-with-an-essentially-undetectable-object-just-outside-its-event-horizon is a very good approximation to a black hole of a slightly larger mass.

(At this point I want to note in passing that any "real" black hole will emit Hawking radiation until it eventually evaporates away to nothing. Since our clock will still not have passed the event horizon by the time this happens, it must eventually escape - although presumably the Hawking radiation interacts with it on the way out. Presumably, from the clock's perspective all those billions of years of radiation will appear in the split-second before 12:00, so it won't come out looking much like a clock any more. To my mind the resolution to the black hole information paradox lies along this line of reasoning and not in any specifics of string theory. But of course that's just my opinion.)

Now, this idea seems a bit weird (to me and I think to you as well) because if nothing ever passes the event horizon, how can there ever be a black hole in the first place? My friendly cosmologist's answer boiled down to this: the black hole itself is only ever an approximation. When a bunch of matter collapses in on itself it very rapidly converges towards something that looks like a black-hole solution to Einstein's equations, to the point where to all intents and purposes you can treat it as if the matter is inside the event horizon rather than outside it. But this is only ever an approximation because from our perspective none of the infalling matter can ever pass the event horizon.

Assume the object falling in is a blue laser that you launched directly (radially) towards the Schwarzchild (non-rotating) black hole that is aimed directly at you and that you are far from the black hole. The massive object is the laser itself, the light that you are watching is your way to "see" the object as it approaches the event horizon.

First of all just because the laser is moving away from you it will be slightly red-shifted just by the Doppler effect. As it approaches the black hole that slight red-shift will become more and more significant. The laser light will go from blue, to green, to yellow, to red, to infrared, to microwave and to longer and longer wavelength radio waves as it appears to approach the event horizon from your point of view. Also the number of photons it emits per second (as you detect them) will decrease with time as the horizon is approached. This is the dimming effect - as the wavelength increases, the number of photons per second will decrease. So you will have to wait longer and longer between times when you detect the longer and longer wavelength radio waves from the blue laser. This will not go on forever - there will be a last photon that you ever detect. To explain why, let's look at the observer falling in.

Your friend who is the observer riding on the laser does not even see anything happen when he crosses the event horizon (if he is freely falling). The point is that the event horizon is not at all like a surface that you hit or where anything unusual happens from the freely falling observers point of view. The reason why there will be a last photon you will ever detect is because there are only a finite number of photons emitted between the time the laser starts to fall and the time the laser crosses the event horizon. So that last photon emitted just before it goes over the event horizon will be the last photon you will ever see. That photon will be a very long wavelength photon and you may not see it until some time in the distant future - how far in the future will depend on the number of photons per second that the laser emits - but there will be a last photon and after that you will not see any more photons.

So, I claim that the laser does disappear from an outside observer's point of view. Note that trying to "illuminate" the object near the event horizon by shining a different laser on the object and looking for scattered photons will not work. (It will not work even if you throw the second laser in to try to illuminate the first laser.) From the point of view of the laser that fell in, these photons will only hit the laser after it has already crossed the event horizon and therefore the scattered light cannot escape from the black hole. (In fact, if you wait too long before you try to illuminate the object, the infalling laser will have already hit the singularity at the center of the black hole.) From the outside observer's "point of view" (but he cannot "see" this), the infalling laser and the photons that are trying to illuminate the laser will get "closer and closer" to each other as they get frozen on the event horizon - but they will never interact and there will never be a scattered photon that you might try to detect.

Everything you say in your question is true, and your comment "the event horizon is in a different time reference" is also true, though it needs to be stated more precisely.

If you've read much on relativity you've probably come across terms like "frame of reference" and "inertial frame". A "frame" is a co-ordinate system i.e. a system of distances, angles and times used to measure the location of things. For example the map grid references are a co-ordinate system used to measure locations of things on the Earth's surface.

General Relativity gives us a way to describe the universe that is independant of any frame of reference. However for us observers to calculate what we see, we have to do the calculations in our frame of reference i.e. in meters and seconds that we can measure. The static black hole is described by the Schwartzchild metric, and it's not hard to use this to calculate things like how long it takes to fall onto the event horizon. One common co-ordinate system is co-moving co-ordinates i.e. the observer falling into the black hole measures distances from himself (putting himself at the origin) and time on the stop watch he's carrying. If you do this calculation you find the observer falls through the event horizon in a finite time, and in fact hits the singularity at the centre of the black hole in a finite time.

But where things get odd is we calculate the time taken to reach the event horizon in our co-ordinate system as observers sitting outside the black hole. This is an easy calculation, that you'll find in any introductory book on GR, and the answer is that it takes an infinite time to reach the event horizon.

This isn't some accounting trick, it means we will never see an event horizon form. At this point someone will usually pop up and say that means black holes don't really exist. In a sense that's true in our co-ordinate system, but all that means is that our co-ordinate system does not provide a complete description of the universe. That's something we've been getting used to ever since Galileo pointed out that the Sun doesn't revolve around the Earth. In the co-ordinate system of the freely falling observer the event horizon does exist and can be reached in a finite time.

You ask:

If this is the case how can a black hole ever consume any material, let alone grow to millions of solar masses.

As long as you stay outside the event horizon a black hole is nothing special. It's just an aggregation of matter like a star. In the centre of our galaxy we have a compact region, Sagittarius A*, containing millions of star masses, and from the orbits of stars near Sgr A* it contains enough matter in a small enough space to make it a black hole. However the orbits of those stars just depend on the mass they're orbiting and whether Sgr A* is actually a black hole or not is irrelevant.