1. Is that explanation likely to be accurate?

Sounds possible but not likely, unless they'd employed a complete
moron to install the drains. It's accuracy isn't relevant though, they
seem to have accepted liability.

2. Is it likely that any long-term damage could have been caused?

Yes, the dampness would increase the likeihood of mould, dry rot,
woodworm etc. The floor void needs to be thoroughly ventilated to dry
it out.
There will be solid, rotting food waste in the floor void, making
vermin (insect & rodent) infestation likely. It needs to be cleaned
out.

Should I get a professional opinion?

Yes. And monitor the condition of the floor void over several years.