I agree with everything you say.
But I'm going to play devils advocate because it's fun.
Filming for this took place last year, information coming from tweets responding to RRs mentions the fact this advert has been around for a while. Peter Philips was "beardless" at Sandringham earlier this month. Is it just a tiny bit possible that the papers did some digging and thought this fits in with our current storyline lets run with it? Is it also possible that with the "abdication" this would never have seen the light of day....
A lot of the filming was done green screen, and Peter himself never uses the word royal at all. The only thing related to royalty is he mentions them having Jersey Cattle at Windsor. The use of the word royal, the mention of the family, Jersey being a royal estate of britain is all added in chinese captions which Peter probably can't read.
Now the correct thing to do, which may have been done, was to view the advert as a whole and then assess the impact of how it looked.
The Queen, Prince Charles, Anne and I guess to some extent William might be fully aware of the whole thing. We'll never know.