I think the key is not degree 2 but rational- matching with rational surfaces is not straightforward - I suspect that when you’ve encountered degree 2 surface matching problems these have been revolved surfaces or similar where the control point are unequal.

The result is rational in this case - a middle control point, per 90 degree arc gets thrown out of line with the quadrant points and a kink develops there. It looks like the position is the one that would be correct for a non-rational surface, which is I guess what you were saying, @davidcockey.

-Pascal