Actually I was buttonholed by someone after a gig a few years ago, and lectured at great length about how suprised she was that I 'could play tenor recorder so well with such bad technique'; eventually I managed to narrow the perceived bad technique down to using straight fingers rather than curved, and had to plead guilty as charged on that one.

As Breukink says, recorders can be made with the fingerholes in-line (assisting flat fingering and "inhaler" breathing) or in arcs (for playing with fingertips and with the arms angled downwards). Look at the tenor in this picture from Praetorius's Syntagma Musicum - use your fingertips exclusively and your hands would end up in a pretty strange position:

http://upload.wikimedia.org/wikipedia/commons/a/a0/Syntagma06.png

I have one like that as well as others with the arcuate layout. They both work.

Here is a player of one of the Praetorius tenors who is Doing It Wrong, no matter what your recorder teacher interlocutor might have said:

http://www.music.iastate.edu/antiqua/tenor_recorder.jpg

Looks awkward as hell and her tone on the sample on that page is feeble, nothing like what that instrument can do.