Stembridge-type coincidence conjecture for hybrid Grothendieck polynomials

Let $\delta_n=(n,n-1,\ldots,1)$ be the staircase partition, and let $\rho\subseteq\delta_n$. Write $\rho'$ for the conjugate partition. Stembridge-type coincidence conjecture. One has

$$G_{\delta_n/\rho'}(\mathbf{x};\alpha;\beta)=G_{\delta_n/\rho'}(\mathbf{x};\alpha;\beta).$$

The displayed assertion is identical on both sides as written in the source, so it is tautological; the surrounding discussion indicates that this was intended as an analogue of the Stembridge equality for stable and dual stable Grothendieck polynomials, but the source statement itself does not provide a nontrivial equality.