Though I would certainly not quote Carnegie Mellon or anyone associated with CMMI as being authoritative when it comes to Agile Methodologies, there *is* a move on CMMI's side to "play better with others," including Agile.
The real question is whether it's actually possible. I'm still forming an opinion on this, but given that I'm dealing with CMMI and that I have some background in the Agile Methodologies, I can safely say that there's more compatibility than you would normally think. Part of the problem is really understanding CMMI and understanding what Agile means.
Unfortunately, CMMI is typically misunderstood because it's rarely implemented properly (which is mostly its own fault...I'm certainly not trying to defend CMMI). When viewed from the perspective of defining a process that has proof it was followed (generating those artifacts), it becomes less of a demon and more of a plan waiting for a good tool (or tools) to solve.
Of course, on the Agile side, there's also a lot of misunderstanding. For example, XP is assumed to be synonomous with Agile, when it's just one of several published Agile Methodologies (of course, it's also the most popular, so there's some expectation of that). In fact, Agility is more an approach to methodologies than any specific practice (though there are some that are implied, such as Iterations). See the Agile Alliance for lots of details (www.agilealliance.com).
As for the "clean-room Agile" reference: I expect they're referring to the creation of an Agile process that is CMMI-compliant (clean-room referring to not bothering to leverage existing Agile Methodologies like XP).
Fundamentally, I don't believe they are compatible in the sense that CMMI requires "proof" that you followed the plan. Agility doesn't require proof. The "proof" is the delivered application, nothing more. There's a fundamental disconnect. However, the question of whether you can do both is still there; not from a philosophical perspective, but from a physical process perspective. I think the answer is that you can (but, it won't be XP), but it's not trivial (and requires a significant amount of tool support).
Dan