Drywall will have adequate strength where sheets are attached to at least 2 or 3 joists on 16 inch centers. Drywall is not stronger along any dimension (width or length) but more than 2 attachment points across a sheet reduces wavyness. It is easier to go perpendicular to joists because a narrow piece can be applied across joists, but not along them. The approach used on this job sounds just fine, and a box frame was constructed where the pipes run. The use of screws will make access to pipes possible in the future with minimal disruption.
Any drywall can show deflection in time if moisture is excessive. Be sure to de-humdify the basement if needed. If you are still concerned, just offer your relative a beer and ask why the sheets arent laid across the joists. Keep it friendly.