I'd say it's safe to assume that as long as the shampoo provides high lubricity and it satisfies you and doesn't marr the finish to oblivion then why not? Because a company suggested you use their product? I understand and respect synergies within product lines but when you get down to brass tacks the mitt does the decontaminating, and the lubricant functions soley as that, a lubricant.
That being said, I wouldn't suggest washing a car from the get-go with your Nanoskin wash mitt. Nanoskin themselves suggest working on a clean, washed car in the packaging. With that in mind, if you just washed your car with a rinseless or the 2BM, why would you wash it again with the mitt when you can work section by section with a lube?
Ultimately, I think it all comes down to preference. I wouldn't use ONR, and I wouldn't use the wash mitt as suggested with a shampoo if I just washed the car. If you're budget-minded, stick to that and try ONR. If you want the best lubricity possible, use the Nanoskin Glide. If you want to wash your car twice in a row, use the mitt with a shampoo of your choice. Just make sure you're not dry rubbing your mitt on your paint.
