Fair enough, but what exactly is your stubborn belief based on?

You are right that the total output of the warm light must be higher since the beam intensities are the same. This could be the reason why the warm light actually appears to scatter more in this photo. Although the beam is the same intensity, it is wider which would mean more scattered light in the beam cross section. However, I think the photo dispels the myth that cool white scatters a lot more.