I think the most important thing is to find a balance- at Championships, I went out scouting for a little while, and at some teams' pit areas you were directed straight to the mentors when you had technical questions, because there would not be a single student who could answer; I don't think that is right.
Last year was our rookie year (tho two out of our three co-captains had been on a FIRST team before), and we had a 'mentor hands-off' policy. Our team was interesting because we were 9 people, and most didn't have any pertaining experience at all, myself included. We were really lucky in that our mentors were understanding, because they taught us everything, without taking over, and now I fully appreciate how difficult that must have been for them; this last saturday, I was with our LEGO team, and it took all my willpower not to just grab the legos and run away cackling madly; i mean, i LOVE legos
! and i bet our mentors felt that way all build season, but for the most part they wouldn't actually pick up something and start working at it unless we asked them- once we asked, they were free to help. And as a result, we learned a LOT. we knew from that start that if we built it on our own, our robot may not be one of the 'winning' ones, the ones that everyone wants in their alliance. but we made a conscious decision that having a 'winning' robot didnt matter as much to us, we just wanted to have fun and learn. as it was, we had tons of fun and learned a lot, and our robot did fine. it is part of a mentor's responsibility to know when to back off (and to do so if asked), but eqaully it is the student's responsibility to willing stick their nose to the grindstone when that time comes; a mentor cannot be blamed for doing it themselves if the students are slacking off.
finding the balance is the most important thing for a team to be successful- i don't mean top 8 seed successful, i mean 'everyone is inspired, happy, and has learned so much that they have forgotten what their house looks like' successful...
just my 2 cents (aaaaaaaa where did the cents sign go? ....can't...find....)