So the reasoning makes it sound like there was potentially an exploit that made it easy to find unlisted videos? Were the video IDs deterministic perhaps?
Edit: Before the scheme change I mean
Block ciphers (such as DES) don't collide. If they did there would be no way to decrypt them because a block could be decrypted into multiple valid plaintexts.
The old scheme had 7.3 x 10^19 ids (11 chars, base 64, thanks Tom Scott!). Suspiciously close to the max value of a 64-bit int, hmmm …
Assume a billion videos and you’re down to 10^10 - a one in a 10 billion chance isn’t much chance, but it’s far from secure.
(I’m ignoring the fact that only a small %age of videos are unlisted I guess, but I think the point still stands.)