I've heard it repeated by rote so many times that you shouldn't do it but so long as you wear the correct type they don't easily get caught. Also, if you don't put your hand in the chuck or bit then it can't get pulled in.

I've been wearing gloves with heavy drilling machinery for 22 years, as they are mandatory in my work. You DON'T want any fabric or stretchy palms, our gloves are nitrile-coated non-stretchy palms and elasticated back. With about 60 employees drilling every day I have never seen a problem related to gloves catching and our drill extensions are covered in stillson burrs.

I always wear gloves when drilling with my bench drill as I don't like getting my hands cut or burnt. For your lad, you could run the belts loose enough to turn the bit but slip if there's a foul-up.