Outdated information in jwt token payload

As written in jwt.io "The payload contains any arbitrary information in the form of claims that we as developers find useful for our applications.". So i think it would be convenient to put there username, email, and so on. In this case i have no need to get this information from database or file system during authentication process. It is being touted as an advantage if app is distributed across many servers.

But I see here is one annoying obstacle. What if a payload was changed as a result of changing user account information? All old issued tokens stays valid since a signature is still valid. So i'll get wrong user account information from old token payload.

I missed something in idea behind jwt tokens?