"Streaming limit reached" -- at ZERO streams!

Man, they really can't get this "single stream at a time" right, can they? I watch across Apple TV, Apple iOS and Web, but they simply can't pick up when I've closed the one device to move to the other. I hard-close the apps as well (swipe up), so it's not like they're still running in the background. Pathetic. This is really not rocket science.