Actually, TiVos get disrupted by EBS signals. Honestly, it's super annoying! It seems that if any channel runs a EBS test, the Tivo responds by kicking you out of whatever you're watching and showing a large banner across the screen for a few minutes. There's no way to stop it or make it go back to playing your recording until it's done. Usually, it happens during the middle of the day. But, this is when I'm on my treadmill watching TiVo shows, so I get annoyed by this about once a month.
I still think you make a good point otherwise, but TiVos do try to play along (maybe they are required by law?).