I never heard that you're not supposed to wear shorts in the rain before. I for one would hate getting wet in the rain while wearing shorts. It's bad enough having to wear them when it's sunny. Wet shorts will itch, ride up between my legs, drip water down between my legs so it looks like I peed myself, and be excruciatingly uncomfortable as I walk and feel my clammy, fleshy thighs rubbing against each other, and sometimes they chafe. 
A little dampness is tolerable, but at this time of year where I live a light drizzle can turn into a huge downpour in less than a minute.