To me the most annoying problem in this protocol is that she's probably going to get one right. There's a 42% chance that she is going to pick the right person in at least one of the three trials through pure random chance. Once she has the right person, she's got a 50-50 chance a of getting the correct side. Thus overall there's a 1 in 5 chance she's going to get one correct. If the left kidney is removed more often, then those odds increase with a guess on the left.

If she does get one right, we'll never hear the end of it.