On the interference engine with timing belt that I have the most experience (BMW M20) the chances of escaping a timing belt breakage incident without valve damage are absolutely zero. The real question would be if we could save the head.
Myself I would have wanted to keep you as a customer so I would have explained all right upfront and not have gone the “lets put the belt on and try it” idea. That is unless I personaly had seen these engines escape timing belt breakage without damage.