I don't believe Bamber would divulge this information to anyone.
He would want to keep the myth going that he is being hard done by, and there are millions of unreleased documents.
This suggests the police are hiding something and the documents may prove his innocence.
CAL probably found this out from another source. Or may have eventually coaxed it out of Bamber.
There is evidence that proves the information was released. By denying it he would be revealing himself to be a liar who is just using a bogus tale of document being held under PII to pretend the government is withholding evidence. Real lawyers won't want to help him anymore if he is going to publicly lie about such.
He has supporters who spread lies on his behalf. He might enjoy them doing about some things but might not enjoy them doing so about others things. While it is assumed he has complete control over the campaign team and other supporters that is clearly nonsense and there is no way to know which things he is pushing them to post or trying to get them to rescind.
If they post something overly damaging then in that case he will be forced to risk alienating them by thoroughly disclaiming their assertions in a press release or the like (personally or issued by his lawyers). But to date he hasn't had any such need their lies haven't risen to such level. He will contradict them simply in a less than public communication.