Correct. They didn't even know if there was a finite number where colouring became impossible, but it was strongly believed there was such a limit. Privately, people had their own ideas - sort of Fermi estimates. I don't know anyone who made such estimates public.

Exactly, the program would have never halted if it were possible to colour all triples.

Worse even, no one would know why it wouldn't halt...

In other words, you have to be lucky to find a counterexample to the given assumption otherwise you're stuck publishing an increased lower bound