Why do surfaces have different "True" boundaries?

While going through the python chapter of the dynamo primer, I notices that when I plot a distributed UV points on a double curved surface, some points lie on the outside of the boundary, resembling a surface similar in nature to the one being plotted, but larger and with the previous surfaces inscribed like a diamond. In the image the blue line is the boundary edge of the original surface, and the blue dots are the UVs evenly distributed on that surface. the larger surface that correlates with the plotted UV is the result of turning the original surface into a nurbs surface. I find that when I do certain operations, such as trimming the nurbs surface with the boundary edges of the original surface, it simply returns a surface that will have UVs that extend its boundaries.

Can I get an explanation of this behavior? Is it because of the isocurve direction of the double curved surface is in the diagonal direction?

If I want to evenly plot out or be able to subdivide this surface, much like the divide surface tool for mass in revit, or maya or GH what is a good approach?

since double curves surfaces can be defined by straight lines i have tried to connect points from the boundary edges, but there must be a better way to go at this?

Related to this issue. Don’t think it’s resolved yet

May not be the best advice, but take a look at the experimental T-Splines