The injected water does not move from its injection site. It gets absorbed by the rock. Some of the water displaces the natural gas that then gets pumped to the surface. The water does not travel at all, let alone travel the thousands of feet, against gravity and through impermeable rock layers, to get to the aquifers people use for water.
Hydraulic fracturing -- fracking or hydrofracturing -- raises many concerns about potential environmental impacts, especially water contamination. Currently, data show that the majority of water injected into wells stays underground, triggering fears that it might find its way into groundwater.
Injected water that remains underground is sequestered in the rock formation and therefore does not pose a serious risk to water supplies.