An important fact about modeling with NURBS. The intersection of two NURBS surfaces usually (there are exceptions) can not be exactly represented by a NURBS curve or other simple explicit mathematical equation.
For situations where the intersection is not exactly a NURBS cuve there is a solution. The intersection can be approximated by a NURBS curve within any desired non-zero tolerance, ie the difference between the approximate NURBS curve and the intersection can be made as small as desired but never exactly zero everywhere. The tradeoff with making the difference smaller is more control points/spans for the NURBS curve. This is one reason why tighter tolerances can result in more control points.
Any software which uses NURBS has the same situation.