I don't think they "allow" Google or Amazon to host them so much as Anthropic itself is deploying and managing their services on multiple cloud providers just like every other global scale business. Even the models served via OpenRouter are just being routed to compute under Anthropic control. Same with OpenAI. They aren't going to hand the world's most valuable intellectual property at the moment to some third party to run independently.

Now for the Chinese models on OpenRouter, yea. Those providers could be legit. Or it could be a failed crypto mining operation pivoting to providing AI compute. Who knows.