Hello,
"What would we do?"...walk away!
If the guy really wants you to do a wet process on it, and you want too, you must tell him what the implications are very likely to be. Put all of the limitations in writing and get him to sign it.
Frankly though, you're really not doing yourself any favours getting into this. Better to explain and educate, do a fantastic job on the other wet cleanable carpets and he will think more highly of you for sticking to your professional expert knowledge and will more than likely use you again.
Be interesting to see what the others on here have to say.?
BF Nicky