In that sense, everything is "fully owned" and the phrase is meaningless. But in the context of the summary where you're using it, it certainly sounds like you are claiming ownership on the infrastructure
Also, I like treating my blog as a version-controlled, declarative "codebase" that's just a bunch of plaintext files (no MySQL tables, XML or JSON to crawl through).
What if it's a dedicated machine, colocated? What if it's at home, but I pay an ISP?
edit: Downvoted, care to explain why? I genuinely wrestle with this question. I self-host lots of services at home - and I also self-host services on a cloud VPS, which have better availability and security posture with regards to my home network for things I make public or semi-public. Some have told me this isn't "self-hosting" and I am not sure where the line is drawn.