We rent from STJ Rental also and never have a problem picking up the car at 10 am. If there is not one ready yet we usually go over to JJ's for bite and by the time we are done the jeep is ready.
We picked up our rental car as soon as Dilbert Hill's office opened... around 8 a.m. I think it just depends on whether or not all the previous renters have returned them or not, I suppose.