People actually feel like they're "taking ownership" of something when they feel at source rather than at effect with it. It is something that comes from rather than to them. When people say they feel a sense of ownership of how things happen in their work, it's because they shape how things happen.
It is a classic and naive oxymoron when leaders say they want their people to "feel a sense of ownership" over something leaders define and impose." No one feels this is actual ownership. On good days people forgive leaders for being so unrealistic and naive. When they act with courage, they take ownership of whatever good they can, often informally which means certainly behind the backs of their leaders.