The time that the Queen turned down a birthday concert from Paul McCartney to watch Twin Peaks

In this excerpt from Secrets from Another Place, a Twin Peaks DVD collection, series Composer Angelo Badalamenti recounts a story he allegedly heard from Paul McCartney.

Queen Elizabeth II's staff organized a private concert with Sir Paul for the Queen's birthday. When Paul showed up, he was told by her Majesty that she couldn't listen to him play because it was nearly 8pm and Twin Peaks was about to start.

The story sounds a little fishy, at least in Badalamenti's telling (I wonder if Paul has ever been asked) and commenters have pointed out things like Twin Peaks was broadcast in the UK at 9pm, not 8. And wouldn't her staff have known her TV viewing times? But maybe at least the kernel of the tale is true.