That's the easiest case.
AWS Bedrock models running in AWS Secret Cloud for Industry. (I really have no affiliation with them, I'm just like... this is a completely solved problem, why do people think this is hard and requires on-prem hardware?)
https://www.aboutamazon.com/news/aws/aws-secret-cloud-for-in...
I'm with GP that these are tinfoil hat concerns, when there are solutions to all of these, unless you're perhaps in some country with very specific needs beyond things like European sovereignty or US military secrets (like a non-US defense concern).
Note that the other commenter never said US-based military oriented startup. You just assumed, then jumped to "heck yeah let's use Amazon Secret Cloud for Industry"
Not everyone has or wants an office in Crystal City.
If I were ranking third parties on their ability to safely handle my data without compromising it, I would rank Anthropic pretty low for things like Fable (where they more or less promise that they will misuse my data), but I want Azure pretty low in the sense that I fully expect them to be compromised.
I would tend to trust Amazon to avoid being compromised.
The provider needs to comply with specific rules, have specific certifications, and sign specific agreements. You check the boxes, and you're good to go.
Microsoft does that better than anyone. OpenAI and Anthropic don't do that at all. Google does that rarely and poorly. AWS is not bad, but not as good as Microsoft.
Azure was always my go-to for regulated applications in the cloud. Some do require e.g. on-prem or even air gap, where even Azure is out.