This is not so in ActivityPub. The data you post is owned by/controlled by the instance you're on. In the language of the article, you're still a row in somebody else's database.

I was on Mastodon for a while until the instance I was on shut down. I naively assumed that I could export and re-import my posts but that was not so. Everything is deleted. I technically have an archive of it in the form of some JSON files, but as illustrated by the article, this is now dead data. The same will happen again if/when my current instance shuts down. The only way around it is to run my own instance, which for the vast majority of people is a ludicrous proposition.