You're not. It's two different meanings of the word. You aren't "responsible" for the running of the business because you've "taken ownership" of the autocomplete widget on the search page. You're getting paid for your ownership of the autocomplete widget, you're not getting paid for your ownership of the corporate direction.
If you're getting paid, you do need to be getting paid because of some responsibility you're discharging, after all.
You can tell it's two different "ownerships" by what happens if you quit. One you retain, the other is simply redistributed to some other developer. They're not the same thing.
