I would say driver. The 5870 is supposed to have a 45W idle draw, is this correct?
I would imagine this state is achieved when the system is set to have the monitor turn off after a specified amount of time in power saving settings. Imagine browsing the web, or in a 3Dgame and suddenly the power saving feature kicks in for some reason. Those gray bars would be something I'd expect to see if that happened.
So, a driver fix, or in a more severe case, a BIOS update for the cards. Meaning the whole 5xxx series line if a simpler driver fix can't be done. It would also be interesting to see what kind of connections most of these people are using. DVI? HDMI? Display Port?
Don't know if that would make any difference, but it wouldn't hurt to know.