I had a bottle of dish detergent sitting behind the sink, and it trapped water beneath it for several days. When I moved it, the granite was dark and discolored where the bottle had been. [...] Is it caused by moisture actually impregnating the surface of the granite?
At the risk of stating the obvious, water isn't dark. Micro-organisms growing in water are dark. Any remaining darkness is probably the remnants or spores of shrivelled, dried-up, died-of-thirst micro-organisms. What you need is some sort of bleach strong enough to bleach organic material but not strong enough to corrode granite. Whether or not hydrogen peroxide falls into that happy medium I couldn't myself tell you, but if the Internet says so it must be true...
Peter