I can't imagine Valve want the extra work of maintaining a Linux distro. Even if it was just a rebranding, they'd still have to deal with thousands of bug reports about hardware and software problems.
There was a vague rumour that they might build a Linux-based games console. That sounds more plausible - by controlling the hardware, they could avoid a lot of problems, and if it doesn't look like a PC, people don't expect to be able to install Windows software. But moving to hardware would still be a significant change.
There was a vague rumour that they might build a Linux-based games console. That sounds more plausible - by controlling the hardware, they could avoid a lot of problems, and if it doesn't look like a PC, people don't expect to be able to install Windows software. But moving to hardware would still be a significant change.