It does, but not like you'd think. If the backup is dormant, the right-to-be-forgotten portions can remain there. Once it comes out of cold storage, those RTBF requests have to be processed over the restored data. Although, in most cases, the dormant backups will expire and be deleted as per a data retention plan.
Which part isn't correct? What op described sounds like a good and easy way to do it (as long as you have sane retention periods) and doesn't seem to conflict with the article you linked in any way (in fact, they agree).
In addition you have to tell the customer how long you retain your backups (and only retain them for a reasonable time) and only restore for purely technical reasons.
This is usually solved by encrypting and throwing away the key or seed to effectively delete.
Tape is no excuse to violating data retention policies.