Beyond the aviation angle of this question there are legal liability and insurance concerns common to any business that ought to be addressed. Any person renting equipment ostensibly for personal use, but in reality is using it to run a business on the side, ought to have a commercial lease agreement in place with the owner of the equipment. Have you spoken with the FBO about your plans?
Regarding aviation specifics, these sort of questions have come up before and the CFRs don't offer much in the way of ownership requirements for aircraft involved in commercial operations. Own vs lease just doesn't seem too critical from an operational standpoint as far as the Feds are concerned. I won't start another "holding out" discussion here, but you should definitely talk to the FBO about your plans before moving forward with this idea.