Hmm, since it was still connected, I again tried to drag a file from my desktop to the Time Capsule - and I got a popup saying if I wanted to do that, I needed to click "authenticate". Except I don't see anything that says "authenticate" other than that instruction!
Then I noticed that in the finder, listed right below "Network", it shows the content ("Data") that is inside the TC. I could drag it inside of that.
Went back to Network to see the Time Capsule and couldn't drag it to the TC, but I could drag it to the "Data" listing inside TC. So I guess there is some consistency there at least.