The only thing that I can think of that would possibly be a problem suddenly going to a healthy plant-based diet is if they're on meds for bp, diabetes, cholesterol or the like. Your body starts to recover very quickly if you make a radical healthy dietary change and amounts of medication that were appropriate on a typical SAD will be harmful and potentially fatal on a lowfat, whole food plant diet. Tapering off and eliminating certain meds must be done with a doctor. For example, Dr McDougall (off the top of my head here) often reduces insulin by half on the second day for his patients and has 90% and more Type II diabetes off all meds within two weeks because they do not need meds any more. It can be that fast.
Sounds like an excuse to me. ;-) Even if there are some allergies, it's a question of finding which plant foods to eat, not a reason to keep eating meat/dairy.