Sounds like BS to me as well, but sometimes they try to simplify what they tell you and come off sounding dishonest.
The thing they may be worried about burning up is the throw-out bearing, and the pressure plate at the point where the bearing rides on it when pressed. However, I would assume that the pedal can be adjusted to allow some play at the top. (Don't have my manual handy and haven't needed to mess with mine.)
If you can jack the car up (in the rear at least), try letting the clutch out slowly to see where it starts to engage compared to full up. (You can do this on the ground but it's easier on the clutch and easier to watch if you jack it up.)
Drive along at 30 in third gear. Dip the clutch, rev the engine a bit, then let the clutch out very abruptly while giving it gas. If the clutch is slipping, you'll know it (and lift off the gas immediately). I hate to recommend this to someone who doesn't have experience doing it, so you might ask someone who does.