I actually consider myself a detailing "expert" so to speak. The dishwash soap thing is an extra step which is not necessary when claying; yes it will strip the wax, but so will clay. Like I said the contaminants are below the wax: common sense that it would remove the wax too!
I did manage a Turtle Wax Company owned full serve wash and detailing center for many years. I did this kind of thing every day; even played around with test chemicals/waxes/polished that were in R&D as well as using many competitor products first hand to compare results by machine and hand application.
'97 Cobra Vert - sold
'06 GT Sold 6/2010
Current: '06 F-250 Diesel, '10 CR-V, '11 Civic (Lease)
Ordered 12/12/12 Built 1/25/13 dealer received 1/30/13
2014 GHIG V6 Stick w/Perf. Pkg