Some of the confusion may be due to the various built-in post features and mod post features not running after an in-line AJAX edit. Hypothetically.
The in-line media mod definitely requires the url parser to have happened, so maybe it only looks in URL tags. And certainly when you edit or quote a post that's got a properly displaying video, you only see the url tags - so maybe the in-line media mod runs on display, not on edit - whereas the url parser runs at edit time and affects what actually gets saved in the post database.
Obvious really