There is no doubt that lots of organics get swept into my pool when it rains - we have a lot of close in trees and the runoff from those definitely has dust and such. Even 1" of rain in a 20x40 pool is a LOT of water (I calculate ~ 520 gallons (20x40/12 * 7.

) - if the organic load is high, that might be like having 10 or 20 uninvited guests partying in the pool for hours - no one would question whether that might be considered a "chlorine needed event". Plus, like others have said, creatures seem to move when it rains, we get tons of worms & millipedes committing hari-kari everytime we get a significant rain.
Way back when, on Poolforum I believe, we discussed this in relation to SWG PH rise, which seems very regional. In my case, I measured the PH of rain water and suggested that it might be a counteracting factor since I had seen no PH rise with my SWG. I still believe this is at least partly true, earlier in the summer when we had no rain, I did have to add acid. Lately, with a lot of rain, no rise - no acid.