It's a believable story. I personally know a few women who have tried some fad diet that eliminates certain foods and ended up with nutritional-deficiency illnesses.
I guess the parents were permissive -- let him eat what he wanted or not eat those things he didn't like. When I was a kid, Mom insisted we eat our vegetables and "cleaned our plate" before we could have any desserts or snacks. This was typical of parents back in the '50s. Maybe parents don't do that now.