The question doesn't say the birthday is on a Friday every year. That would be impossible, anyway. Nobody's b-day is weekday-dependent. I'm going with the 7/4 or 12/25 theory.
The day after Thanksgiving doesn't make sense, because you would have TWO possibilities, Zachary Taylor (Nov. 23) and Franklin Pierce (Nov. 24). Yes, I had to look it up and check it against a perpetual calendar.
The question is not phrased as though there is a choice, so it must be something else.
Good point. Must be the 4th, then. See #66 to HEY4QDEMS.