It appears FHA looks down there for moisture during an appraisal:https://birminghamappraisalblog.com/appraisal/fha-appraisal-red-flag-water-in-the-basement/Maybe some Appraisers can weigh in on this.

Moisture and Texas heat more than likely has this home filled with mold, not to mention all the critters (termites and other bugs) that probably made this their home. 

It can usually go right over existing flooring, and note that some floorings may need a moisture barrier, like cement.

Ive never had a mold or moisture complaint in this house. 

If you are able to redraft another lease (again, this depends on the area), you can make sure that there is specific language in the lease about making sure they are properly ventilating the home and doing things like limiting number of plants, etc. that may cause moisture build up.

Clearly there was a moisture problem at some time but it didn’t look like a present problem.

I go and inspect and there is literally no leaks upstairs, no water lines in this section of the house and no rain for days outside and no sign of moisture intrusion from outside.

Is the spot next to a sliding door where moisture could be an issue?

Inspection revealed improperly shimmied joists and structural sagging, furnaces were 31+ years old (seller would not replace), moisture behind some of the shower tiling, chimney need mason work done and looked structurally suspect.

The money he thinks he is saving by doing it himself may be eaten up in extra repairs inside due to moisture damage.