No, you're not wrong. But I would go further and say JWTs should be obsoleted by using an object-capability model (see: http://habitatchronicles.com/2017/05/what-are-capabilities/ ) which is a more fleshed out way of using unique unforgeable "tokens" to access things. The ocap model is tailor made to solve the problem that CSRF is an instance of (confused deputy attacks).