We agree in principal.
I merely extended your point. Imagine some long lived reference data which could even be username/pwd or permissions. Those could be cached on every server in memory and kept in sync via { insert magic of choice here }.
Given the above, would looking up info in memory violate statelessness? If not, how does looking it up in a remote db violate statelessness? If so, there are very few stateless _apps_ in existence.
I assume something like claims sent with a token is considered more stateless than looking up authorization in a db.
I've always taken the stateless dictate to mean something like:
Given POST /foo followed by POST /bar, there is no server state that "knows" POST /foo occurred "recently".
That is subtly distinct from POST /foo altering application state such that POST /bar is possible. So POST /bar doesn't try to check if you have done POST /foo, it checks whether POST /bar is possible given the application's current state.