Sure, you can own your server and have it at home. It must be nice to have enough space at home to dedicate some to a server room (servers are noisy btw). But many people live in small apartments in a city and so don't have that luxury.
You can own your server but rent some rack space from a data center to put it into. That would still be self-hosting.
You can rent a virtual or dedicated server from a hosting company, and even that would be self-hosting.
The author seems to not consider the fact that this is a spectrum but also, from a practical standpoint, mostly the same thing.