The notion that you cannot box in MMA gloves is nonsense, the kind of thing a coach lacking in historical knowledge or context (or who has never spent significant time in a boxing gym) would perpetuate to make themselves seem uniquely knowledgeable. The "broken hand" moment demonstrated would have resulted in a broken thumb for for either glove, because the punch was fundamentally incorrect. Remember, I had an amateur fighter snap his thumb in half in a TWELVE ounce glove due to improper point of impact. It wasnt his fault, his opponent made a weird reaction, but the glove did nothing to prevent the break.
Then he proceeds to do a demonstration where he just consciously hits harder with one than the other on a bag. Now sure, it has been demonstrated that without bigger gloves, fighters are a bit more wary of their punches, but it's not on cue. Hand breaks are very very common in boxing and this notion makes it seem like theres a world of comfort punching with 8oz gloves. There isnt.
Also, boxing has been around far longer than foam padded gloves. Those are a very recent invention.