I love Medium. It’s a fantastic writing tool. I wish, more than anything else, is for Medium to have an API. This would allow for the development of a WordPress plugin, a Drupal module, etc. that would allow Medium to be “the network” you mention above, while still allowing me (the author and copyright holder) the ability to publish on my site/blog first and syndicate out to Medium.
The way it is now is that I have to publish the same content in more than one place, which is not ideal.
What you have built is amazing, but it’s a closed system. A walled garden. You offer no hooks for Zapier or IFFT to connect to which could automate the syndication of content from my own source to Medium.
If you truly mean that Medium is a network, then you’ll treat it like a network and knock down the walls to your walled garden, or at least open up some doors so that I’m not forced to choose between publishing on Medium first or my own site.