So here is an image with the perfect NURBS circle defined:
And when you zoom in real close, with a very coarse display setting, you can see how the curve is meshed into line segments (Marked here)
So note if those little mesh points were actually connected with the curve value, that they run through the endpoint of the line you have connected.
Also, if you zoom in to this level, and then change the wireframe display settings to very high, you will see the curve actually move into the intersection and appear connected...