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...
For prompt caching, they already say they permit it, and do not consider it "logging" (i.e. if you have zero retention turned on, it will still go to providers who do prompt caching).
The underlying provider can still limit rates. What Openrouter provides is automatic switching between providers for the same model.
(I could be wrong.)