Related? There are also missing Beatles performances that were also recorded over by the BBC — one of which (do I have this right?) made an appearance in an early Doctor Who episode? I think that Doctor Who episode is still in tact.
Ironically, The Chase often has rights clearance issues when it comes to home release because of this. Beatles music costs a fortune to clear, making releases untenable.
Double ironically. This is because the Beatles chose to mime to their studio record for Top of the Pops. If they had played live, it would have been less of a problem.