Nope, you still need to trust the system. It doesn't know the exact data, but it does know the decision process for generating output based on the encrypted data. That means that just like unmasking people using TLS to connect to websites, the metadata (what decisions are possible / which ones are taken / when they are taken / who is doing the processing / the time in which it takes to process that data / the time the data was queued for processing / etc.) is important and can be used to defeat the encryption even without decrypting it.
Worse, assuming the data is unique enough, it may even be possible for a compromised host using FHE to corrupt the data in a way that is beneficial to an attacker. Due to the increased processing time requirements, (and associated charges that go along with it), those using FHE are unlikely to be inserting poison pills to frustrate such attacks. (As it would have to be done on the data owner's side, because the host processing the data can't be aware that the data it's working on is fabricated for the poison pill to have the desired effect.)
All FHE is really useful for is hiding the generics, or those adjacent enough, during the early days of deployment. Before more sophisticated analytics are developed. That and convincing bean counters and C-Levels that they can "safely" continue using read: paying these cloud companies for a few more years, before they'll be forced by the pendulum to take stuff back on-prem.