Prof disagrees with assigned textbook regarding an exam question

Do professors have an obligation to recognize the assigned textbook as an authority in the context of the course?

No, there is no such obligation. It's a bad educational practice to choose a textbook that's seriously unreliable, but even good textbooks slowly go out of date, and they sometimes have a lack of detail or even outright errors as well. It's important for professors to try to be clear about any deficiencies the textbook has, for example by highlighting them in class. I provide a written list of any typos or other issues I am aware of (although I note that of course there may be others as well). However, there is no obligation to accept the textbook's version as a correct answer, and there are no specific rules about how things must be brought to the students' attention. It's entirely up to the lecturer's discretion.

I would expect that many professors would be more flexible or accommodating than what happened in this instance, but not all of them. At least in the sort of universities I'm familiar with (in the U.S.), there's no way an administrator will change the grade under these circumstances if the faculty member who assigned it is unwilling to do so.

On the other hand, it's not clear to me from what you say whether this person is a regular faculty member (due to the lack of a Ph.D.). If you are dealing with a teaching assistant, it could be worth asking the professor in charge of the whole course. This will probably upset the TA, but it might work (since the professor will want to maintain common policies among all the TAs assigning grades). Other than that, I don't see any recourse.

Added in light of Pete Clark's answer: I'm assuming your answer is definitely wrong. I.e., either the textbook had an error in it or it's out of date regarding a clear scholarly consensus. On the other hand, if you can make a case that your answer is actually correct or accepted by serious researchers (not just that the textbook says it, but that authoritative and up to date scholarly sources agree), then you've got more of a basis for disputing the grade.

My opinion -- as a university teacher for four years pre-PhD and eleven years post -- is that your story is balanced precariously on the border between "unfortunate" and "actionable". What is to be done about this probably depends a lot on your national and local university culture, the culture of your department, and even on the judgment of your own instructor.

Here is some advice about how to best deal with the situation:

I sent an email to my prof with the page number and the exact quote from the textbook that supports my answer.

That is already not the ideal strategy. This is a matter that requires some discussion, and email -- especially email exchanged between people who don't know each other well -- is not conducive to discussion but rather to one-sided statements of position, often of a nature which is more definitive, defensive or combative than a person would be in a face-to-face meeting. You should go to physically meet with your instructor. It is not too late to try to do so.

"In class I said that correct exam answer... This is an issue with any text and shows why class is so vital: Texts rapidly go out of date or (such as the broad text used for this course) demonstrate a lack of depth. Lectures are usually much more up to date."

That's a pretty good answer. If the textbook is incorrect, superficial or out-of-date on the point which was covered in the lecture, and if you did not attend the lecture, then you are showing that you did not receive and learn the information you were tested on.

Keep in mind that this is an Archaeology class, which in my unprofessional opinion really doesn't "go out of date" all that quickly.

Definitely don't say that again. This sentiment is indeed unprofessional. It is also ignorant and insulting: academia is about the progression of knowledge, not just keeping it preserved for posterity. Archaeology is no different from any other field in that manner.

The online lecture notes posted by the prof make no mention of the disagreement.

That is not definitive, but it makes me more sympathetic to your situation.

I was not present at the lecture.

That's bad. You have every right to expect that when you miss lectures you miss critical information. That's desirable, really: otherwise what's the point of lectures? By any chance did you contact the instructor and ask to be updated on what you missed? Did you get notes from some classmate that did not include this point? Either of these would mitigate your absence (the first more than the second).

Do professors have an obligation to recognize the assigned textbook as an authority in the context of the course?

No, of course not. On the contrary, they have the obligation to correct the textbook when they feel it is helpful and/or necessary to do so.

In my experience, when confronted with such a problem they typically go "Ok, fair enough, I'll give you the mark", but are they just being nice or are they supposed to do this?

I agree; "I'll give you the mark" is the more typical, nicer reaction. Not to do it is being a little callous, in my opinion. But it is unlikely that "they are supposed to do this", at least not officially. The instructor of a course has a certain amount of authority. This decision, although it may not be a "nice" one, seems to fall within that authority, at least in my experience.

He's not a senior prof (not even PhD yet), so do you think going to his superior would help?

At most universities I'm familiar with, someone who does not have a PhD is not a "professor" at all. But that probably doesn't really matter: what matters whether he is the "instructor of record" or a "teaching assistant". (Probably: in some places, one does in practice have more or less classroom authority according to one's academic rank and seniority.)

Yes, going to his superior might help. But you should think very carefully about this and have at least one face-to-face meeting with your instructor first. Before you do that:

Find out whether your answer was actually correct, or arguably correct.

If it is, you'll have much more of a leg to stand on. If it isn't, if push comes to shove...well, we mark the right answers right and the wrong answers wrong, don't we? Finally:

If I get this one extra mark it will bump me up 0.4 GPA for the course because I'm right at the cut-off.

This is the line that tipped me over a bit into recommending that you pursue the matter at least a little further. It is one thing to mark a question wrong because it is wrong. It is another thing to stand on this to the extent that it lowers your final course grade. There's a proportionality issue here: yes, you were apparently wrong to go with your textbook rather than the instructor. But were you that wrong?

It seems likely to me that some more senior personnel in the Archaeology department will feel the same way. If you can find such a person, then maybe they can influence your instructor. However, if you are very confrontational with your instructor then he may be inclined to stand on principle, even in the face of senior personnel. You really want to make changing the grade the easier, more palatable option for all involved.

"In class I said that correct exam answer... This is an issue with any text and shows why class is so vital: Texts rapidly go out of date or (such as the broad text used for this course) demonstrate a lack of depth. Lectures are usually much more up to date."

Well, your lecturer is right. Text books are sometimes factually wrong. If he indeed pointed out the error in class and you were not aware because you did not go to class, you can hardly blame the lecturer.

That being said, most lecturers would probably be open for a sensible argument, but you should certainly approach it as a nicety or concession of the lecturer, not something that you can force by applying to some sort of obligation.

He's not a senior prof (not even PhD yet), so do you think going to his superior would help?

Rank doesn't really have a lot to do with it. Going to his superior (if such a person exists, which may depend on how your university works) may help, or kill your cause entirely. In my home university, complaining to the department head was generally a horrible idea. Department heads never decide against a lecturer in a case that is not a clear-cut violation of university policy. All you would do in this case is make the lecturer much more unsympathetic towards your cause.