All the things you've heard are consistent and together they answer your final question by denying that there is a discrepancy in choice of theory, just in choice of name. (Not that I'm sure that all the things you've heard are true.)
That would make "TDT is underspecified" a rather odd thing for someone to say, though.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Thread started before the end of the last thread to ecourage Monday as first day.