Are faculty hiring committees overly polite on "denial" answers

This sounds like a standard US rejection - they may be sending this exact same text to all other candidates that were rejected. I do not believe you can learn anything from it and it does not reflect on you specifically in any way.

You can, however, try to get feedback, but it can be quite difficult - you must realize that the chances of getting good sincere feedback are not high. It is probably best to try getting this from someone with whom you felt there was a good connection or that this person was relatively open. Probably this person would prefer to do this over phone rather than by mail. You may also want to look at this question.

Are they being polite saying that? How much should I trust this kind of information?

Yes, in general the goal of the email is to inform you of the search results in a way that is polite and avoids any not strictly necessary emotional distress, confrontation, antagonism, and (this being the U.S.) risk of litigation. Sadly, this comes at the cost of depriving you of meaningful feedback that would actually be helpful to you. Thus the statements in the email may be completely true, or completely false, or somewhere in between... there is just no way of knowing.

Note that your problem is a common one for job applicants both within academia and outside it, especially in the U.S. where the job application process is especially fraught with potential legal consequences, and where the culture strongly favors euphemistic face-saving politeness over blunt truth-telling (at least compared to some countries I'm familiar with, though other countries are even worse in this regard). See here and here for some related discussions on Workplace.SE.