In the software development field (and I'm sure other fields as well), we have this notion of "ownership" that means something more specific than lay people would expect. If someone "owns" a subsystem, they are not just responsible for it, they also have the authority to modify it, and they understand it well enough that they can modify it. Most often (at least in startups) the owner of a subsystem either implemented it or implemented substantial portions of it.

OK, this is on topic, I swear. This notion of ownership can apply not just just to individual contributors but scales up to teams and even larger organizations. A team can own an entire major system for example.

Software organizations of any size at all need a process in order to ship usable software. Well-run software organizations don't just have a process, they own that process as in the sense above. The organization has the responsibility for the process, they have the authority to change it, and they understand it well enough that they can. Obviously such an organization can respond to deficiencies in the process and adjust it to work better. They can even revamp it completely if they need to.

Your Agile software development process isn't going to work well if you organization doesn't fully own it.