Articles like ones by this publisher require the user to be logged in to read. This translates to the API in the form of require a Cookie header that includes the sid and uid of a logged in user. The header looks like:

Cookie: sid=...; uid=...;

The values can be retrieved by logging into Medium and looking at cookies in the web inspector.

While this does work, it adds back the 3 article limit for premium articles. Articles fetched after that are truncated. One way to get around this might be to use a premium user's cookie, but I'm not about to ask or encourage anyone to give money to Medium.