The answer is yes!
Rain does not make the windows dirty, dirt does!
Dust and dirt accumulates on the glass from pollen, car exhaust and many other sources. Dust and dirt settles on the glass to create a fine layer covering the glass. When it rains, drops of water make contact with the dirty glass. The dust and dirt is moved around too form dirty marks when the water dries. The dirt is now highly visible because it is no longer uniformly spread, but is now sporadic on the glass.
Your windows are not completely clean when using traditional methods (Mop & Squeegee)
When using old methods there is a fine layer of washing up liquid left on the glass where dirt will stick too and rain will mark the glass.
Rain is actually pure water, the same water used in water fed pole window cleaning.
Here are two videos explaining the process: