The browser extension is how an ordinary page behind a login gets onto a screen. You sign in as yourself, add the page with Save Authentication ticked, and the session it saves is what stands in for the person who would normally be sitting there.
Where Screenly renders that page on its own servers, the saved session was not being used the way it should. Some pages were captured logged out, showing the login form instead of what is behind it. Others worked at first and then quietly reverted to the logged-out view, once the site set a cookie of its own. And some failed on and off with nothing to explain why, which is the version that costs an afternoon.
A saved session now does what it looks like it does: the page is captured signed in, it stays signed in, and it holds up on sites that set their own cookies. When a page does fail to capture, the message names the reason instead of reporting only that it failed.
The same applies to a Cookie header you set on a web asset yourself through the API or the CLI.