You dont need a reciept like -aggie- has mentioned. But they do check the SN against the apple database.
I only know this as while waiting for my genius appointment there was a lad infront of me with a Pair of 3gs. The guy at the genius bar put the SN into the computer. Then asked the guy if they were his, A few mins later the manager was there and told the guy to do one as they couldent be sure if they were stolen and they would not undertake any work unless the guy could prove that they were his.