We don't have basements here in the Dallas area or anywhere much in Texas that I'm aware of. Just looking at your photos' though I have a question or observation. Why is there no moisture on the backside of the carpeting tackstrip and only on the front side. Sure appears to be evenly distributed looks like.

As far as the advice you mentioned giving to them, did you give them also notice at the original inspection that these are things that could possibly happen that you have no way of observing if done correctly at the time of the inspection?

Rick