Do you need a commercial certificate to fly unpaid for a non-pilot owner?
This situation would be Illegal as the law stands. What it boils down to is that flight time is considered compensation. This answer covers it well and in your case, since you are not paying your pro-rata share and the owner is paying the full expenses you are in a way getting compensated in flight time. 

This answer is somewhat related as well and its seems there needs to be some "common purpose" for everyone on board as well.