Hi @Charles ,
I filed this as https://mcneel.myjetbrains.com/youtrack/issue/RH-68931 for future reference. The control points or where you see the verts in box mode with the SubD are what are getting aligned to the curve but I agree either verts or ctrl pts ought to work. The workaround currently is to make a surface with the circle and then use Pull instead to get the verts on that…
I also have this request on file https://mcneel.myjetbrains.com/youtrack/issue/RH-55054 to make edge loops circular. I’ll add this post to that too.