You could keep that assumption and just serve a random video if some external IP dials a non-existent ID.
Presumably, no one would do that except researchers trying to count videos (or randomly find hidden ones?).
You can break the assumption of unicity (if an unassigned ID is later assigned) if you do that internally, although not sure that’d be common but it’s not an assumption that has to be strict for non-attributed ones, and you never use the fake ID.
This is easy to detect, though, at least for public videos. Click through to the channel on a different IP and find the video link, or search for the video's title and description, or find a canonical link to the video by any other means. If the IDs don't match, it's been faked.
Presumably, no one would do that except researchers trying to count videos (or randomly find hidden ones?).
You can break the assumption of unicity (if an unassigned ID is later assigned) if you do that internally, although not sure that’d be common but it’s not an assumption that has to be strict for non-attributed ones, and you never use the fake ID.