Well, this.....
"Jessica Kielhorn, a meteorologist technician with the National Weather Service in Reno, said it likely was a result of dry and dusty weather leaving cars dirty and the Sunday night rain not being heavy enough to wash the dust away. There also was pollen in the air, she said."
....is not what I (nor others I spoke to) experienced.

As I was driving, only occasionally using my wipers, the dirty drops of rain would dry on my windshield. I'd then use washer fluid to clean it, and then it would happen again. So, it was in the rain water, not from just the car already being dirty (which, I admit it was).

I even found some of these dried drops on a brand new, black plastic dust pan I left outside.