We use Dawn dish soap in our facility, basically the same formula as Ulines industrial dish detergent. Its a nationally recognized branded product that is clearly intended to clean food contact surfaces, and it saves adorable baby seals. We would never use it for CIP, but for cleaning removable equipment, its purpose is to remove soil so that our validated sanitizer can effectively do its job. All detergents/soaps should be completely rinsed off whether they are from Dawn or from EcoLab.
If you have proper sanitation procedures in place (wash, rinse, sanitize) and can validate that those procedures are effective, I don't see the problem.
In the case of this auditor, simply having dish soap in your facility doesn't seem appropriate cause for an NC unless you failed to provide an SDS or were storing it inappropriately.