This is actually a side effect of the text message backup that's been in place since WP8.0. The device that has the SIM gets the new message and pushes it up to Microsoft's servers to backup. The device without the SIM sees a change in the server backup state and pulls it down. Therefore, it looks like both got the message.
If you really pay attention, you'll notice there's a delay between the time it takes to sync over. And the phone without the SIM won't be able to respond.