Understandable assumption if you haven't been paying attention to Apple and privacy, but incorrect:

https://www.apple.com/legal/privacy/data/en/sign-in-with-app...

>When you use Sign in with Apple on Safari, Apple sees when you sign in to a website so that Apple can authenticate your sign in, but Apple does not retain a history of what websites you sign in to or when you use Sign in with Apple.

I can lie too.

Tell me more! What evidence do you have that Apple is lying?

Lying would make money. Apple likes money. Apple has a lot of money. Many other companies that were in positions similar to Apple have been caught lying. The reason for that was money.

Do you understand how easy it would be to prove Apple lied about that if they did?

Yes, very difficult, probably impossible