When I was doing the quest, I obtained the marks her niece told me about AND I stole the statue. So I had both options when talking to her. Did you not have the option to ask about dropping the statue down a well? (Or hole, or in a fire, or whatever)
Nope, she just forked over the cash. As I recall I didn't even pick up the statue until she had.
Couldn't you sell it to a fence and then buy it back?
Nope, I buy it back, and it's still marked as "stolen."