In Québec, Canada, we would never say the key fits the lock. The lock is definitely not wrapping the key around itself. We say 'the key fits in the lock' - just an other variation for your compendium.

As an example of the even-handedness that makes NZers such remarkably effective peacekeepers, it is not at all unusual to hear both here, "the key fits the lock", and "the key fits in the lock."