One more thing I'd point out, might be of interest. The date on the graph (thanks, btw) is 5/15. Skies are overcast all over the Phoenix Metro area today.
UV index is still at 10. It will stay that way through most of the summer (I've actually seen it hit 11 in the papers...during monsoon season.)
It's even more overcast here (AL).
If you can, open this .pdf file
http://nadp.nrel.colostate.edu/UVB/publications/uvb_primer.pdf Page eight (8) shows UV measurements for a clear day and a cloudy day, same place. Pretty much lays the issue to rest... Except: thin clouds and thick clouds can have different effects.