  In a recent paper by Beaton et al, it was proved that a model of
self-avoiding walks on the honeycomb lattice, interacting with an impenetrable
surface, undergoes an adsorption phase transition when the surface fugacity is
$1+\sqrt{2}$. Their proof used a generalisation of an identity obtained by
Duminil-Copin and Smirnov, and confirmed a conjecture of Batchelor and Yung. We
consider a similar model of self-avoiding walk adsorption on the honeycomb
lattice, but with the lattice rotated by $\pi/2$. For this model there also
exists a conjecture for the critical surface fugacity, made in 1998 by
Batchelor, Bennett-Wood and Owczarek. Using similar methods to Beaton et al, we
prove that this is indeed the critical fugacity.
