I think what has happened is that the stone has not been able to breath and caused moisture to be trapped inside.

YOU have allowed the mold to develop by not fixing the moisture problem.

The inside people came to check the moisture level. the woman had 2 moisture meters, a small one, a bit larger than a remote control, and one with prongs on an extendable rod for reaching the ceiling.

If condensation has built up under the plastic your basement is not currently sealed and you'll have moisture problems you'll want to address (tiles, vapor barriers,sumps).

Don't get the engineered stuff because if you puncture the veneer and moisture gets in it, it will buckle and swell.

Seeing how these porcelain (infused with plastic} planks are installed, I don't see how the floor could be waterproof, as it seems moisture could easily slip through the crack between the tiles.

Should I value my potential time lost, the stress, and expense this instance could cause when the tenant can nick pick everything wrong and harass you, damage your property, make it hard and inconvenient to gain access for inspection or regular maintenance,  call any number of housing authorities with no recourse.The tenant can argue the home had moisture and a potential mold problem, it was hot and HVAC wasn't working properly, there was risk of electrical issues making the property uninhabitable for that period.  

It's an inferior product and if moisture becomes an issue, you'll have to redo the whole thing.You can usually save a lot of money on lumber by buying from a building supply store (lumberyard) instead of Home Depot.  

I can also purchase information pamphlets on mold/moisture and lead-based paint that I am required (by federal law) to give to tenants upon move in.

Should I pay the 5k+ out of pocket to remove all flooring/drywall etc to remove all material where moisture has been present?