Is there no problem dumping grey water on the ground in campgrounds? My grey water doesn't have food particles or grease. It's only hand soap, or dishwashing soap.
Dumping grey water on the ground is illegal in most instances and prohibited in all CG's I've visited. You could face a fine if caught. At the very least, grey water usually smells bad, no matter what is or is not in it. IMHO no LEO, EPA officer or court of law is going to be swayed by your rationale.