Thanks for the vid.
The reason I don't consider D-plane having much impact on putting is because the ball is rolling end-over-end so quickly and any flight time is basically nonexistent. I just think D-plane as being a 3D plane having to do with the flight of the ball, since there's no ball flight to speak in putting, I don't D-plane in putting.
As far as start direction goes, Pelz and Co. have been preaching that face controls about 85%-87% of the initial direction for years. Putting and D-plane can have that in common, but I think it practically speaking ends there.
I could be wrong, but I consider the D-plane more complex than just describing the initial start direction of putts.
I think trouble with a certain direction of break might have more to do with the players proclivity/bias towards misaiming the putter face. I also can be wrong about this too.