Not needing a DB connection to verify means you don't need to plumb a DB credentials or identity based auth into your service - simple.
Being able to decode it to see its contents really aids debugging, you don't need to look in the DB - simple.
If you have a lot of individual services which share the same auth system, you can manage logins into multiple apps and API's really easily.
That article seems to dislike JWT's, but they're just a tool. You can use them in a simple way that's good enough for you, or you can overengineer a JWT based authentication mechanism, in which case they're terrible. Whether or not to use them doesn't really depend on their nature, but rather, your approach.