Gabe Newell has said that he would have no problem if EA wanted to put Origin on Valve's SteamOS. Valve aren't following the traditions of Sony and Microsoft, and don't want to put any limitations on permitted content for the Steam machines.
Speaking on Reddit, he said it "would be fine" if EA wanted to put Origin on it.
We're trying to make it as open as possible.
If EA wants to put Origin on it, that would be fine, etc... (trying to pick an example of something that people think we would prohibit).
Whether or not EA will actually put Origin on there is a totally different matter, but it goes to show that Valve aren't interested in having everything designed for them, and we might see some cool third-party apps as well.