(I am not a mathematician, bear with me) (splines are a major source of heartburn)
I think you are missing a point - you need four.
Ignoring the optional “start” and “end” points that define arrowheads, a spline needs four points followed by zero or more sets of three points or spline = (endp)? (startp)? POINT (triple)+. (note POINT)
Each generated spline segment needs four points. When considering triples, the last point in the previous set is used as the fourth point. (poorly worded).
Note that the spline points are NOT “draw a curve through these points”. For a non-mathematician (me) spline points are “draw a curve using these points in a magical/mathematical way that does not touch, but uses them for guidance”.
Graphviz seems to usually generate 7 (4 then 3) points for simple curves (ignoring arrowheads), but 4 points work fine.
See also: Fun with edges!