Most organizations are going to be self hosting on aws, gcp or azure... So as long as you use their inference services as your LLM then you can keep it all within the private network
I felt like "Confidential Compute" tech could solve this issue once and for all but I'm not so sure after seeing some of the attacks people can do with physical access.
Another option of course is to not use cloud at all and have your own rack in a locked room with a good security system and/or armed US person guards.