I don’t buy the “last minute booking, confusing websites” argument. It’s the parent’s responsibility to make sure they are sitting with their child when they book the flight. (My guess is they were trying to save a few bucks and figured they could cow somebody else to accommodate them).
If it’s an emergency flight, then take it up with the airline.
That is exactly what I think is going on.
Make the asked person look like the bad guy for not being accommodating and the parents the victims because the other guy is mean and said no, instead of the parent being greedy and manipulative.
Manipulators know EXACTLY what they are doing.