Tbh, not even that is guaranteed. Lemmy (or the fediverse in general) are really not that privacy-focussed at all.

While the people running your instance might not be sifting through your data, nothing would stop anyone from doing so. Everything you post on Lemmy is public, and even if all major instances would somehow block scraping (which they don’t), a scraper would only need to create their own instance and ActivityPub would just deliver all of the data in a nice and easy to process way.

The big advantage of Lemmy is that it is not controlled by one large corporation (and instead by a bunch of faceless, unknown randos on the internet), not that posting stuff publically visible on the internet is somehow more private.