Hmm, I don't know. I'm skeptical of that claim, which would imply allergic reaction being more prevalent than lack of an enzyme (which is in low capacity anyway). I've always learned its the other way around, but I'm not saying that is necessarily right. I've never looked into it before.
Anecdotally there is some things that lead me to believe your professor is wrong. Namely, that if the allergic reaction was predominant than this manifestation would be more common while the patients were children. Since lactose intolerance is generally a problem of aging, and as we age we have less lactase in the digestive epithelium, it would be counter-intuitive to think most cases of lactose intolerance (we see most in adults) are from allergies.
More anecdotal; can't say that I have ever known anyone with an allergy to milk (this would be a huge deal and drastically alter their life from the time they were a baby). Nor have I yet to a scratch test come up positive for a milk allergy, but I haven't seen that many scratch tests yet.
Anyway, could you ask your Prof for more information or look into it? I don't have time right now, block exams in T-minus 96 hours!