Interesting question here. Admittedly, I have not thought of it much until now, but I would consider the ABC example to be 'hedging'. Hedging means to make something more polite, and less blunt.
In that sentence, I can easily say "This is for C/This is actually for C", but the 'happens to' softens my comment a little bit without being too 'mean' to A, who ate the meal without asking.
Regarding alternatives to 'by chance', this phrasing 'happens to be' the one that I would substitute as well. :-]