There are one-off posts on Medium, I don't see the significant difference between a Publication and a blog on Blogger or Wordpress.com. Controlling the domain is definitively not required to have a blog.
Perhaps that publishing on Medium grants Medium (through some TOS terms) the right to republish and reuse anything published there (nominally for creating indexes and recommendations, but the legalese says what it says.)
Well, that would mean they've signed two contracts which they can't fulfill simultaneously, but it wouldn't make the original posts a copyright violation, only the subsequent redistributing that Medium might do.
