Yeah, P&G is doing some interesting things with sourcing stuff. Currently they outsource all bar soap production (Ivory, Safeguard, Zest, Olay..) to an outfit that is called the St. Bernard Soap Company, which took over their original plant in Cincinnati. (If you're ever in Cincinnati, poke around Ivorydale....it's a very interesting time capsule of early 1900s chemical production plants). This lets St Bernard Soap do private labeling etc, because as liquids/bodywashes grow in popularity, bar soap was a bit of a declining business. P&G kept liquids and bodywashes to themselves (production fits very nicely in line with light duty (dishwashing) and heavy duty (laundry, Mr. Clean)...just like Colgate (Palmolive...Softsoap...)
I'd wonder, though if they would produce Oxydol....yes, yes I know Redox was the spin-off of a former P&G brand manager (just like LensCrafters was in the beginning) but I'd really wonder if P&G would let their premium technology out in a "bargain brand".