It's not enough: let's say you have signed XML transactions from your bank, so you own your accounts because you have a provable balance and transactions in your own hand, but... You still know just you. The bank knows the finance of anyone, so it can makes informed decisions you can't make.
Let's say you downloads all news articles you read in an accessible, searchable etc format, let's say a feed reader storing posts, and them are full articles in the feed, plus you have historical archives downloadable like old usenet exports. You still get only certain news, others have access to much more news so might know things you do not know and decide to not publish them to take advantage other all the others...
In finance there is insider and outsider training defined and forbidden for a reason, but nothing exists for information. Alphabet or Apple have an immense knowledge from iOS and Android users any of their user have not. How easy for them could be find talents in schools thanks to their education penetration and an ads at a time convince them to take a certain path they like, not necessarily the child like, than hire them while pushing others let's say uni students of some humanities with ideas they dislike in bad roles? What if the owner of an insurance company is also the owner of an insurance comparison service?
We can't rule nature, we can't design a forever perfect society, but as much fairness there is as much positive evolution for all we might elicit. As much as we came back to feudal like society as less positive evolution we might hope.
Of course owning our information, like our home, car, .... is MANDATORY but far from being sufficient. And actually if you see trends... The 2030 Agenda where "you'll own nothing" it's already there in the IT world, it's already there in modern connected cars and so on, it will be there soon in the whole society and that's the topmost asymmetry of information and ownership we can imaging.