I don't really get this American desire to make cemeteries uniform and boring. Who cares if it's Spongebob, of a life-size statue of the deceased? If the family thinks this is the best way to remember her, than that's how it should be.
The cemetery, of course, is within their rights to have their rules. However, once the question was asked and answered, going back on their word is jackassery. Sorta like ATF approving your application for a firearm design, and then turning around and declaring it a machine gun after you already made it.
As far as the employee having or not having the authority, that isn't really the family's problem unless the employee they asked was the guy mowing the grass, which I kinda doubt was the case.