The thing with that kind of family story in "Spare" is, Harry can get away with saying whatever he wants. No one, apart from William can corroborate that sausage story. Harry knows that William is unable to come out and refute it. Therefore he can say things like "Willy got an extra sausage because he's going to be King one day". It fits his narrative completely.
Anything he says that happened behind closed doors can be taken with a massive pinch of salt. He's such an obnoxious, spoilt brat that I can imagine him replying "well I'm a bleeping Prince, witch, now gimme my sausage". But obviously he'd never tell us that bit.
I never understand this logic. Of course William can refute the stories that come out about him. The RF don't keep quiet about this stuff because the are poor hard done by souls who have no way of defending themselves. They keep quiet because the only way they get away with all their
tit (dodgy taxes, multiple homes, jewelry 'borrowed' or 'gifted' from around the globe, political meddling, treating the plebs like shite, not actually doing anything worthwhile ever, being besties with sex traffickers and dictators etc etc etc) is to maintain an air of mystique that sets them apart from the general population.
They can say whatever they like and defend themselves however they please (and when something actually matters to them they absolutely do say something about it) they don't bother to refute any of Harry's claims because they don't care enough about what he's said to do so and they know full well that nothing he's said will bother the public enough to turn against them either.
(Which isn't to say that I believe everything H and M have said, I'd imagine like anyone else it's a mix of truth, lies and misinterpretations viewed through their own lens. But I dont think they're any better or worse than any other members of the RF - Andrew excepted, he's just worse)