Hmmm, we didn't even look at age when reviewing applicants -- so I am not I sure I buy your argument that a school would "flatly reject" someone based on age. Further, I am not sure if that would be even legal (in the US).
I know of a few departments that do it, and some professors as well (1). I'm sure not all do, but I think it's pervasive enough to worry about.
Regarding legality, I actually made a mistake when I said reject due to age. I meant reject due to having stale ideas and not appearing committed enough, or just not standing out from the crowd.
(1) Admissions process at many places: committee weeds out the weakest and professors/groups pick their students from the remainder. If a professor in your field doesn't like 30 year olds, you failed to stand out from the crowd.