WHAT????
Please tell me your source for the information that water from a hose is harmful. In every place I've lived, the hose bibs at my homes were connected to the same water supply with the same type of conduit (copper or PVC, in some cases) as my kitchen sink and every other place where water was connected. A rubberized or plastic garden hose might - and I say that from an excess of caution - MIGHT impart a smell or taste to the water it delivers and there is a possibility that dirt or insects can inhabit the hose, but it it is flushed for a couple of gallons or so, I see no reason to believe that the water is contaminated enough making it unsafe.
Of course, if you live in a area where gray water is supplied by the municipality for irrigation and IF your water bib is connected to gray water, BI ALL MEANS DO NOT USE IT FOR DRINKING OR WASHING DISHES.
It was unclear to me from the OP just how you planned to use the outdoor sink. Are you just going to wash off the heavy gunk before taking dishes inside where they will be washed? Or, are you planning to wash them in the outdoor sink and reuse them there? If the latter, use one tiny drop of chlorine bleach in the wash water and rinse them thoroughly. That should be a lot more hygienic than most people experience when camping - especially wilderness camping.
As with any food safety issue, however, if in doubt, leave it out!!!!!!