While we know Disney have effectively acquired it purely by accident, I would not be surprised if the entire physical archive is somewhere at ITV - I'm presuming with this logic the Game Show Story documentary was an internal ITV Studios production and not an Indie.
It was a Shiver production, so yes, in-house at ITV. But that show was a piece of light entertainment and the TVS Catchphrase clip just used in a montage to represent game shows in general rather than a specific piece about Catchphrase and TVS - so, good though that doc was, they clearly weren't spooling through acres of tape and ploughing through acres of paperwork to find it and digging out rare footage, it was clearly very easily available.
Presumably it's a bit like the Mike Smith situation, it's perfectly possible to show clips from them under fair use, but showing the whole programme is much more complicated.
Yes - the paperwork is irrelevant for a "fair use" clip as there are no rights to settle, if any fee is paid to the distributor then it is purely for the admin involved in providing a copy. Equally fees can be paid to somebody other than the distributor for a copy if it's convenient, as various YouTube'rs will tell you; presumably if a fee was paid for access to this Catchphrase master then it would have been on that basis.
As might have been discussed here once or twice before, proper full-length distribution is impossible because there is no record of who should be paid what.