Very poor wording on my part. Yes, you must yield the intersection to the car on your right. But the one on the left is the one that's going to kill you, because once you both try to get through the intersection at the same time, you have no escape route other than a very sharp right turn. If you mistakenly start moving when the driver to your right does, you can stop, turn left, or turn right, giving you three possible ways to avoid a crash.

(I looked this up in the Illinois driver manual, and it gets a size-negative-a-million one-bullet-point mention. No wonder nobody can use stop signs.)