Ownership is a powerful dynamic in any organization: people see a problem, they just fix it. No questions or squabbles about whose job is whose. No arguments about who gets the credit. The problem, large or small, gets fixed when it's identified.
That's all really good - to a point.
In addition to this level of "can-do" ownership, there must be a feedback loop established. Otherwise, you'll have teams of people who continue to fix the same things over and over and over. A feedback loop will help you see patterns - system breakdowns, simple processes, little incidentals - that can be addressed and fixed for the long haul. Ownership that is valued will result in positive change - not over and over, but rather consistently.
Don't just fix it.