They also had a plastic moisture barrier laid down, but over the 2x4s (directly under the wood flooring.  

There are some moisture barrier treatments which can be applied to basement walls.

If they are not opening windows moisture is going to be trapped in the home and cause mold.

It's not so much a question of what is better - laminate or vinyl (plank or sheet), but what types of flooring are applicable to your situation.While quality laminate (AC3 - AC5) offers a "good looking", functional floor for the price, it does not handle moisture well and can be noisy for tenants below (depending on the sound deadening measure taken in the floor/ceiling boundary).Vinyl tends not to mimic wood as well as laminate {if that is the look you seek}, but it is non-organic, so a good fit for humid or wet areas (bathrooms, laundry rooms, basements, direct over slab, etc).  

Show you care, some respect it will go a long wayTake you're time with these "little bars of gold hidding in the street" they all need your help, the ones that don't respond to you forget about, the ones that do will softly and gently cry out to you and as the process plays out will ask you to buy there home. 

By that I mean anything from moisture testers to infrared photography for heat loss.Well worth the money.John Rogers

Otherwise, significant moisture will be residing around your basement walls for prolonged periods. 

Buy your own infrared camera to inspect the internal moisture levels? 

I would love to move beyond (but not abandon) my primary residence conversion strategy within the next couple of years, and I think a gentle prod in the right direction from some like-minded BP-ers will really help.

Typically when there is a perfect line cut around the drywall it is a sign of some type of moisture issues.