I would add to that the buyer should make it contingent regardless of who pays for it because no matter what - you still want to have that option back out - and to be honest - this is already covered under the "Contingent on Inspection" clause and any inspection that reveals something that the buyer doesnt like is cause for them to cancel the contracts as long as they are within their inspection period and haven't removed the contingencies - so as long as you have included that clause ( which in california is the default ) then you still have enough flexibility to protect your interests.
RE: Selling Your House - Who is Responsible for Termite Inspection ?