Should I reward points for an incorrect answer if it is the result of misinformation presented in a TA's office hours? So a TA came to me asking for advice. He gave wrong information in office hours leading a student to a wrong answer. 

The TA showed the student how to solve the problem via the wrong statistical test - the assumptions for the statistical test he used do not hold in this case. The answer generated from this test yields a test statistic that doesn't make any sense when you think about it's meaning. Kind of like if you were asked to "find the length of the fence that encloses ..." and your method produced the answer of -50 meters. The TA provided the student with step by step instructions, but did not do any of the numerical calculations. Had he done those calculations he would almost certainly have caught his mistake.

The student complains that she should not be punished because her TA made a mistake. TAs can change HW grades, if they have good reason to do so, and this TA wants to correct his mistake by rewarding the student the points on the problem. I told the TA that I would get back to him as I don't want to give my advice in haste. I think I want to say something like this. 

to the TA: "Thank you for asking for my advice in this situation; it is indeed a difficult position to be in. However, this situation concerns me, not because you gave wrong info or bad advice, as we all occasionally make mistakes, but because you seem to have told a student the method for answering the question. While it's OK for students to get help from their TAs, it should only be by reviewing concepts and asking them 'leading questions' that nudge them in the right direction. Note I am not saying that what you did is objectively wrong, as I should have been more clear in my instructions at the beginning of the course, but in the future telling students how to do a problem, in my opinion, is unfair to the students who can't make your office hours."

to the student: "Your TA contacted me recently about changing your HW grade. While I sympathize with your situation, and understand that it is very frustrating to receive bad advice/information from your TA, it is ultimately your responsibility to make sure your solution is reasonable, and therefore I can not give you full credit on this problem. Ultimately the majority of the points you lost were not for using this incorrect method (the TAs error), it was for not interpreting your answer and realizing it made no sense. As stated on the first day of class and in the syllabus I require all students to interpret their answers to make sure they make sense. Please come see me if you would like advice on how to check your answers as this is a very important skill in all scientific disciplines and in life in general. TAs, solutions manuals, and even professors make mistakes. Never trust something just because it was told to you by someone with more authority."

Is this the right thing to do?
I agree that in principle, the student is responsible for critically evaluating information from all sources and rejecting any that's incorrect.  I wouldn't simply award the student points for the incorrect solution, but on the other hand it seems unhelpful to just mark it wrong and leave it there (and despite your explanation, the student will likely perceive this as unfair).  In similar situations, I've done one of two things:


Allow the student to revise the answer, and regrade the problem; or
Discard the problem for that student, and recompute the score for the assignment based only on the remaining problems.