In his presentation, he shows a quadrant which contains 4 different types of cultures:
And he defined certain characteristics for each culture. Look the characteristics for a control culture:
Look now the characteristics of a Collaboration Culture:
These really look like Agile, right?
Look now the characteristics of personal and impersonal cultures:
These one's REALLY looked like Agile on the left side and CMMI on the right side. It is clear that CMMI would fit a control culture much better than a collaboration/cultivation culture and , inversely, Agile fits perfectly on collaboration/cultivation cultures. It's clear how Agile is "Personal", while CMMI is "Impersonal".
So what about compatibility. From the perspective of culture, what is the result of combining them?
I can imagine a couple of scenarios. In a collaboration/cultivation culture, applying CMMI would push the organization culture towards a more Control/Impersonal culture. From the other side, a control organization (which may be CMMI certified, as it's totally compliant) and wants to become more Agile may encounter a CMMI an obstacle.
So in the culture context, I see the 2 forces going in opposite directions.