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  It's a bad educational practice to choose a textbook that's seriously unreliable, but even good textbooks slowly go out of date, and they sometimes have a lack of detail or even outright errors as well.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  I.e., either the textbook had an error in it or it's out of date regarding a clear scholarly consensus.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.