Yes-- same with bluetooth or ordering groceries for delivery and giving your home address. There’s always ways to leak data and make it no longer anonymous. However, from my knowledge of how some of these datasets work, they aren’t putting in a lot of effort into truly trying to make sure the joins are 100% accurate because it rarely matters. They generally don’t give a shit about you as an individual. The most common uses of the data are for advertising and mistargeting doesn’t cost enough to justify the time to verify the data.
Paying in cash though can make it anonymous, or by using virtual cards that mask your card id.
Ahh, Google’s tried and true method of throwing a million half-baked features to people before promptly cancelling them all. This will definitely work for them.