Youtube video ids used to be just base64 of a 3DES-encrypted mysql's primary key, a sequential 64-bit int - collisions are of zero concern there. By birthday paradox it's about as good as 128-bit UUID generated without using a centralized component like database's row counter, when you have to care about collisions.

However theft of the encryption key is a concern, since you can't rotate it and it just sat there in the code. Nowadays they do something a bit smarter to ensure ex- employees can't enumerate all unlisted videos.