How to tell if wall got waterdamage?
It sounds like you are getting very questionable advice. 

Wet drywall needs to be cut out and replaced. Damp drywall is a prime source of mold.  Cabinets that are bubbled halfway up have major water damage and may not be easily repaired.

You should consider getting an independent inspector to assess the damage and the repairs needed. If their view is significantly different from the position of the plumber (or his insurance company) you can try to get them to pay for the cost of inspection.