I figured it out now.
I'm using coat. The problem happened because I generated the curves by converting freeze to curves. This created a single curve which LOOKS like two curves, but when you try deleting some points, you'll find it's actually one curve. I discovered this when I started deleting points on what I thought was the 2nd curve, the two curves joined together at the place you see there.
To fix it, I made 2 versions of the curve, and deleted one of the rings from each of them, and then created a hierarchy so the inner curve was the child of the outer curve. Then did the "right click/fill with mesh layer" and it worked great.
In the future, it would save me a ton of work if it actually generated 2 curves. I could create the parenting relationship myself, but needing to create my own copy, and deleting so many points is rather cumbersome.
STILL! It's a super awesome feature, and even though it's buggy like this, it will still save me a lot of time.