This suggestion has been implemented. Votes are no longer accepted.
I just took a look at it myself. The hat is not upside down, it is inside the hat that is baked into the Saxton model.

As I just said, the hat on these models are not actually hats and can't be removed when a different hat is equipped. You would need to edit the model to remove the hat. The attachment point for the head is also inside Hale's skull rather than on top of it.

It looks ugly to me and I think it is better to not have it at all.

The hat is inside Hale's other hat, but it is also upside-down.

You can clearly see the dangle pointing in the wrong direction, defying gravity.

It would look significantly better if it weren't upside-down, but since this is a problem with Saxton's model, I understand not bothering to fix it.

Still, it would be nice to have the hat on the other bosses, assuming they also do not end up upside-down.