Hang on, I'm a bit confused here.
Ann has a key. Ann must know that the key is Bob's key. If Ann isn't sure that the key is Bob's key there's a bunch of bad stuff that might happen.
So now Eve can get the metadata, and be pretty sure that the stuff sent to Bob actually is sent to Bob, and not someone else, because it's encrypted with Bob's public key.
Eve can't decrypt anything. But my post wasn't about Eve getting any content, it was about Eve getting metadata that's cryptographically tied to an identity.
Where am I going wrong?