I'm not sure I understand what you mean by inference provider here? The inference workload is not shipped off the compute node once it's been decrypted to e.g. OpenAI, it's running directly on the compute machine on open source models loaded there. Those machines are cryptographically attesting to the software they are running. Proving, ultimately, that there is no software that is logging sensitive info off the machine, and the machine is locked down, no SSH access.
This is how Apple's PCC does it as well, clients of the system will not even send requests to compute nodes that aren't making these promises, and you can audit the code running on those compute machines to check that they aren't doing anything nefarious.
The privacy guarantee we are making here is that no one, not even people operating the inference hardware, can see your prompts.