I suppose the quality of rainwater depends on where you live? It could have pollutants in it or I suppose it's possible it could be less damaging than municipal water because it doesn't have chlorine and all the chemicals. When my grandmother was young they collected rainwater for various reasons, including bathing. She said rainwater was the best, soap worked better with it... could have been the times though!
Greywater is wastewater from pretty much all the ways we use water (bathing, dishes, laundry, ect.) except toilet water. Not to say that rainwater is always pure and clean, just that is not greywater.