There's one step I just can't get.

Fbar gets tails, and Wbar gets the result OK. Why?

Wbar is measuring the state of Fbar's lab against a basis that is the subtraction: (wave function for heads) - (wave function for tails).

So if Fbar gets tails, I expected Wbar to get fail.

Probably I don't understand what it means to use a basis that subtracts one wave function from another.

I am sure this must be a dumb question, but can anyone help me?

Reference

"Quantum theory cannot consistently describe the use of itself"

Daniela Frauchiger & Renato Renner

DOI 10.1038/s41467-018-05739-8

Nature Communications