Clearly no-one is going to investigate whether a DIY claimant on a sportive was actually signed up as a participant. So AUK might be validating someone who is parasitising an event held on public roads.
The alleged recent case of 'cheating' on PBP is a case in point. A fast finisher was held to be paced by a non-entrant, who went on to post a Strava track describing it. I'm not as bothered about that as I am about similar behaviour on LEL, where interlopers make it necessary to secure access to facilities, giving control staff another job to do.
If people are going to run more lavishly-catered Audaxes, which fill up rapidly, then it's probably not a good idea to allow DIYs on other paid events.
However, I don't really see a problem with Sportive riders carrying Audax cards issued by the organisers. I can see that it might breach ACP rules, but a suitable designation might be found.