I happened to be near Walmart a few days ago so I stopped in to check out the sun hats.  There it was as Deathwind mentioned.  A very Tilley-esque hat.  Near the top of the crown is a mesh band all the way around, but only .75" (19mm) wide.  I would prefer more mesh area but will see how well it works. 
There is a small pocket in the inside of the top of the crown with a hook & loop closure.
It was marked $10.  Unlike Deathwind I paid $10.
Seems like a good hat for the money.
My wife recently noticed a large sun hat in Costco.    
Sun Protection Zone .  Looks well constructed but there is only one size and no adjustment.  She will be trying it out this summer.