Sort of. If you opt out of their paywall nagware stuff your posts don’t appear anywhere on the site other than your own feed.

Technically you can opt out. Realistically if you do then you lose all of the benefits of being on medium

The biggest benefit of being on medium is that I can just write some words and push the button and I get a nice-looking web page I can share with my friends. I don't care about google rank or more eyeballs or whatever. But I'd rather focus on writing better words than worrying about the words -> website process. Give me something that's as easy to work with (log in, type stuff in the in-browser editor, push publish - no renting a server or installing ruby or whatever) and looks as good at the end, and I'll happily use that.

That's been around for ages:

http://blogger.com http://wordpress.com

Or self-host wordpress