claim that it is decentralized

Yeah, the truth is a bit more complicated.

1. Some objects not not decentralized. For example users are only federated. (there are some ideas brewing to improve this but right now they are not).
2. It is decentralized between "homeservers" (sort of like instances) not end users. But this is really just an optimization and good for privacy. They do have prototypes of running a homeserver on your phone along with the client. So most clients only talk to their homeserver. But your instance works with federated and decentralized objects (depending on the type of object).

But I think the key thing here is that rooms are decentralized and can survive sever losses. If I create a room on matrix.org and matrix.org disappears it can still be fully used by other servers. (As long as at least one other server was participating when matrix.org went offline, much like you need 1 seeder to keep a torrent alive.) Of course if all admins were accounts on matrix.org then the room will no longer have any admins, so it may be crippled, but if there were admins on multiple servers then the room can effectively live forever and survive any number of homeserver losses.

This is very different from federated protocols like ActivityPub as you can probably tell where the death of an instance will kill any communities on it.