Feel your mirror sometime when you're driving in traffic at night on the interstate and it's been dimmed because of the vehicle following you for some time...it will be perfectly cold.
The electrochromic material between the panes goes through an oxidation/redox reaction in the presence of a voltage. In circuit, it functions something like a low-storage battery or capacitor. It does not have enough leakage current to cause it to get hot, that's just the effect of the sun on the plane.
The person you are replying to sounds to me like they put their hand on a window and it was hot.
So not for the reasons you rule out, but they have experience, you have theory.
The person that responded to that didn't say it was impossible: they did convey that the reason it was hot was not due to the window itself. The heat could easily be from the light being absorbed by the panel.
> that's just the effect of the sun on the plane.
This would the area where it could just be the effects of the sun.