I recorded a VC and shared the link with my students. For some reason, some can access the link and for others they get an error message 'Not Authorized You do not have permission to access this item'.

By default, the recording is set to allow only those individuals with predefined access to the meeting room will be able to unlock the recording with their username and password. You can modify the permissions on the recording to be public, meaning anyone who clicks the link will be able to view it, but you can also put a passcode on it, or you can move the recording to the content library and then give permissions to view it as any other content object.

It sounds to me like you may have predefined access to your room for some students and let others in as they came. This would explain why some could access and other couldn't.