I think they meant keep a low profile from the government, not customers. Anthropic is doing the opposite by loudly asking for regulation.

If the company is "hot" attracting a lot of users, then of course the gov't is going to come knocking too. They're going to want access to all of that user data even if it's not a service they could use directly. Sure, you don't have to go courting government contracts, but it's not like government employees are not going to see the same PR civilian users see.