If you are kind to him and replace the unit, be prepared to do that with ANYTHING he wishes to complain about. If there are not burn marks on the outlet or did not find a significant voltage drop (which would in turn increase the current draw on the unit), I do not see how you could be responsible. Seems to me you are in the rental business, not home warrantee business. Might suggest he purchase a home warrantee to cover any of his appliances. But, of course, good luck with that.
Another thought, if you do choose to replace the unit. either remove the outlet or put a faceplate on it making it unusable so he cannot do it again out there. There are other things that can be a problem - such as close lightning strikes. Those effects are unpredictable outcomes, sometimes simple.