Should we worry about the 3-sum decomposition?

Stream: Seymour

[Martin Dvořák]

Does the hard direction hold the way it is stated now?
https://github.com/Ivan-Sergeyev/seymour/blob/4f3d17b1b2e62f4ab7423e684cb1254a61208cd4/Seymour/Results/HardDirection.lean#L7

I found a presentation that made me nervous:
http://matthiaswalter.org/downloads/Talk-TU-Misbeliefs.pdf

Namely, slide 7 says:
image.png