General way it's done in the States is you pay for everything, and I mean everything. In some places, like in the Bay Area, the renter pays for fuel after the flight. You receive all rental income, but pay $10 an hour to the FBO for their management skills. Often the FBO will want you to purchase fuel off them, and also use them for maintanance. More profit to the FBO and less choice for you. Make sure you are 100% sure what you are getting yourself into.
Usually only worth doing if the value of the plane is going up, or as a tax write off. If it was a sensible thing to do the FBO's wouldn't be so keen to offset all their risk to the owner of the plane.
If you really want to become a plane owner and offset some costs you should talk to some of the clubs in the San Diego area. I think there might also be some members clubs at LGB. Another idea is renting off these clubs to time build.
Have you found out what the demand is likely to be for those planes? Wouldn't expect it to be too high in LA. Don't listen to the FBO, they aren't taking a risk like you are, and their reasons for doing it are not the same as yours.
Forgot to add, when you rent your own plane, you will pay the FBO the full rental rate + sales tax. No discount for you, and you still get to pay the FBO it's fee for renting the plane to you.
Good luck.