I had my own tricky situation in Y with my 2 year old last week. He was very tired and freaked out with the belt on at push back. Of course it was a flight when taxiing took 30 minutes. He was kicking and screaming. I just had to physically restrain him for those 30 minutes (not too difficult with a 2 year old). It got so bad the air stewardess came over after being told by the pilot to take their seats to try and help me calm him. Luckily I had some understanding fellow passengers around me. Once airborne he was fine.
Anyway point is you need to be prepared to make sure kids have belts on or suffer the consequences. Of course I don't know what the medical issue was here that could have made life more difficult. I suspect the note didn't say they shouldn't wear seat belts but was instead being used to justify why they didn't want to wear seat belts.