Depends. The core issue is that a lot of developers confuse authentication and authorization. And oauth kind of muddles the water on that front by vaguely doing both but not really. All it does really is exchange tokens (assertions).
Anything JWT related is orthogonal to oauth. Oauth does not actually provide any semantics for the tokens you exchange. They might be JWTs and you might be able to verify them. Or they might just be some random number, a hash, or some kind of database id. But you would have to know in advance what it is exactly and what the proper process for verifying the token is.
In the case of a random number or some kind of session id, the process of verifying that token would involve looking it up from some kind of database or via some kind of API.
Alternatively, with a JWT, it might be a signed one (hopefully) and you'd be able to check the signature if you have the public key. All you have at this point is a blob that was signed by someone that you might or might not trust. The claims and other meta data in the token would tell you hopefully who the person is (authentication) and the level of access they might be given (authorization). The JWT spec defines some fields that you might use for that. But it's up to you to check all those things and verify them.
The point is, that a lot of this stuff is simply implementation/vendor specific and you just need to know what to check and how and why. And it's on you to do all those things.
This is not an issue with oauth, or JWTs, but with incompetent developers doing things wrong or being lazy/negligent/indifferent. Which sadly is very common. Lots of people that get busy implementing all sorts of stuff without any formal training. And a lot of this stuff isn't even taught properly in schools/universities.
This falls in the same category as putting passwords plain text in a database, not setting up ssl certificates, running your database on an open port on the internet, and similar things that developers do wrong all the time. Because they don't even know the basics of how to do things right. A lot of these things would be caught during any half decent audit. And quite a few of those things could expose the companies involved to some expensive law suits. Which is why lots of companies spend money on audits because they don't like expensive law suits.