How true is the stereotype that PhD graduates are overqualified?

First things first - this question is very region- and field-specific, as cultural norms and views of academia differ a lot in different places. Further, this will naturally also be highly employer-specific, as not every recruiter or employer has the same sort of requirements, views and prejudices. Everybody who tells you that there is a hard and fast rule is lying.

That being said, there are a few observations that I think are pretty general w.r.t. the PhD job market:

• Nobody hires you or pays you more just because you have a degree. It's a pretty common misconception that having an advanced degree somehow magically entitles you to higher pay even if you do the same job in the same quality than somebody without a degree. This is particularly pronounced in computer science, where there are a bunch of excellent programmers / software devs out there without degree. Don't expect to make more than them just because you got your training in an university rather than through participation in open source projects.
• At least in central Europe, no smart person does not hire you just because you have an advanced degree. I am confident to say that in Switzerland, the sentiment expressed in your quote is entirely wrong. A PhD certainly does not close any doors. There are a lot of jobs where it will be useless, but I have not yet seen cases where it was actively bad for the applicant to hold a PhD.
• There are a bunch of jobs out there where holding a PhD is in fact very good for you, even outside academia and research. Here in Switzerland and IT, consulting is one of those fields. Consultants with PhD look smarter on paper, and hence their time is easier to "sell" for horrendous amounts of money to customers. It is pretty well-established that in this case just holding a PhD will in fact give you better starting salary and better career opportunities in many companies.
• Generally speaking, as a PhD holder, you will have less experience than somebody who worked in the industry for 5 years. Contrary, you should (at least hopefully) have a higher level of formal knowledge and understanding of underlying principles. What you need is either (a) a job that requires the latter rather than the former (various "evangelist" or innovation jobs come to mind), or (b) and employer that has a time horizon large enough to allow you to get experience and who has problems complex enough that they need somebody with deep fundamental knowledge. This is the reason that big tech companies such as Google, IBM, or MS, often also pretty aggressively recruit IT and math PhDs, rather than going for cheaper and more experienced professional software devs.

I'm just going to address this part of your question since I have direct experience with it:

You've also got less jobs to choose from, since you're vastly overqualified for many and you probably won't be able to find any good entry level positions because people will just assume you'll get bored and leave as soon as you find something better

It depends how in demand you are.

I think there are three sorts of jobs you can get after your degree. The first type are jobs where you directly use your degree. In this case, your degree is an asset: you would be unlikely to get the job without it and you have a strong advantage against another candidate who doesn't have your degree.

In the second case, your degree is either neutral, a bonus, or a small minus compared to someone with equivalent experience. The specifics will depend on the actual job description, the actual experience of your hypothetical counterpart, and the specifics of your degree and field.

The third case are jobs for which you are vastly overqualified. Let's say you have a PhD in chemistry and you're applying for a job as a lab assistant, or you have a master's in English and you're applying for a job as a shop assistant. These are the jobs where someone is likely to believe you are going to leave as soon as you get the opportunity.

I have a couple of friends with PhDs who struggled to get work in the recession, and were turned down for Type 3 jobs (in the UK) because they were overqualified. The irony is that yes they would have preferred something better if they had been able to get it, but in reality they wouldn't have had anything better to leave for, so they were not in fact the flight risk that the potential employers thought they were.

So type three jobs may turn you down. But if you're in demand enough, you won't need to apply for type three jobs, so it won't matter. It really depends on your field.

Although the accepted answer starts with a disclaimer, it ends up painting a rosy picture. That's certainly not my experience in the US job market, as someone who studied a very pure field of mathematics and then sought jobs in finance. There are indeed some hardships faced by PhDs that can make it harder for the reasons exactly stated in the Quora snippet. The reasons are somewhat valid in that a PhD program isn't really about training you to accomplish things in the quickest way possible, which in the Real World is often what is desired.

However, having a PhD will open doors too, generally by companies/managers who have enough experience with academics to know the pros and cons. It's a mixed bag, like a lot of things.

I think the warning for the number of jobs being limited is true. There are many jobs where they will immediately assume you applied accidentally and throw out your resume. On the other hand, same is true for having a Master's too for some jobs.

Believe it or not, the hiring managers dismissing your application may actually know more than you. You may be desperate and really, really want that job doing glorified paperwork, but that hiring manager has dealt with someone just like you before, who left shortly after getting a much more interesting job.

As a word of final encouragement, things aren't as bad as they seem, but often they seem worse to PhD graduates, who lack the training and experience to seek jobs in industry. I think the most important thing for any PhD wanting to go into industry is, have a plan as soon as possible, at least a few years before you graduate. It doesn't take much in the early stages of your grad school to take steps that will end up moving you a lot closer toward that industry job. One that comes to mind is summer internships.