FWIW this is highly unlikely to be true.
It's true that the upstream provider won't know it's _you_ per se, but most LLM providers strongly encourage proxies like OpenRouter to distinguish between downstream clients for security and performance reasons.
For example:
- https://developers.openai.com/api/docs/guides/safety-best-pr...
- https://developers.openai.com/api/docs/guides/prompt-caching...