Andyross
Yes because with this type of "recording" it was never stored on your own hardware, but rather om THEIR hardware.
It was (in essence) an access link.
Likewise in the recent dispute between YouTubeTV and Paramount/CBS, it had been announced that if Paramount/CBS was dropped, all "recordings" would be removed.
For this purpose, these purported recordings are pretty ephemeral, like kissing a hologram insted of kissing a real person.