YOU WANT IT THEN? I'm sorry to hear that, it's not your problem that they are 1 seat short, and as i pointed out, from a legal point of view " There has to be a seat for a 3 year old".
Like gate4lounge, I would have shown them the boarding pass and (nicely) advised them that they should not visit their problems on you.
And if they insist, I would (again nicely) advice them, that their legal foundation for such a solution is marginal to non-existent.
I would probably have risked an offloading, by insisting on the seat for my child, nevertheless, I would have done it.