Well, I've been thinking about that original point...that the "apparent temperature" or heat index, is higher in sun vs. shade, and I'm afraid I just don't know enough about all the various coefficients that go into the rather complex formula for heat index.
I'm thinking that there may be something to that, as obviously your body is absorbing more solar radiation in the sun than in the shade, thus heating you more quickly. But what I don't know for sure is if that is accounted for in a lot of the various coefficients in the formula or not, so there may or may not be a point there.
It's fully possible the effect of direct sunlight may be already be accounted for in the coefficient values dealing with skin.
His comment disregarding the guy talking about humidity being the bigger player, and that H.I. does not go below ambient temp is dead wrong however.