It's certainly critical part of everything that entails "owning". When you own the domain you have control of the full URL of your content so no third party will be closing/changing the location of your published content. You could keep your content in post its and "own" it regardless of its lack of URL, but as far as published content goes, having control of its lifetime is a big part of owning it.
Switching URLs for stuff you've written is more of a re-publishing of the original content, but if it happened without your consent (SILO going down), then you have to re-create new posts with your old "content".
Of course, you also need to have some control of your storage, and usually free options sacrifice some of that. The combination of controlling the location and storage of your content would be pretty much "owning" your content.