Ledger is subject to European data retention law, and their backends are fully capable of recording how much cryptocurrency someone has.
The European data retention law certainly wouldn't apply if their backends aren't actually receiving this data..
However that might well be that of a third party, or their own but without any unique/linkable identifier being transmitted with the requests.
Certainly these endpoint have no authentication / user accounts though, and I don't think it'd be easy for some low level hacker to associate an IP address with a specific person.