Firstly, they should be running in archivelog mode, no question. Relying on Export/Import is a disaster waiting to happen.

Secondly, constraints can help performance -- never mind about the very modest impact of validating pk's, not nulls, and fk's, because you probably SELECT data many many more times than you INSERT or UPDATE it. Constraints help the optimizer produce a better execution plan, and can be created as "deferrable" anyway should they need the ability to temporarily suspend them during a transaction.

It sounds like they deserved to lose some data.