The author was having a little fun calling it a “lie”, it’s more like a popular simplification. The question is how to join Bézier curves smoothly, and it’s fairly common for people to join them by matching the velocity, which means if you join two cubic segments (for example) with control points [a,b,c,d] and [d,e,f,g] where you’re joining at point d, then setting d-c == e-d, which puts c,d,e in a line with d as the midpoint, will connect the two curves smoothly. Lots of Bézier curve editing software will have a mode that enforces symmetric control points around the join point. The problem, or “lie”, is that this symmetric strategy doesn’t match the 2nd derivative, so there can be an abrupt change in curvature at point d. You can have a smoother join by adding constraints like curvature or 2nd or 3rd derivative matching, and that’s what the article goes into - one way of achieving smoother matches.

This WP entry mentions several other alternatives to smooth joins besides matching curvature:

https://en.wikipedia.org/wiki/Composite_B%C3%A9zier_curve#Sm...