False.
I already said this, but here's a link to the page. The PDF of the actual course standards is linked at the bottom of the page. Feel free to read them, if you don't believe me. I don't know about any other agency, but the SDI prerequisite for Nitrox is to be enrolled in an OW course or have OW or Jr OW - which is also notable. A person with Nitrox could only be certed as Jr OW. Even if they got Jr OW a long time ago, that and a Nitrox card doesn't mean they have OW. If they are only enrolled for OW, there is nothing that says the person has to do the Nitrox course even with the same instructor or shop that they are doing OW with, much less that they have to complete OW before the Nitrox card can be issued.
Computer Nitrox Diver Course | SDI | TDI | ERDI
Do I think it has ever happened? No. Probably not. But, as a dive charter operator (if I were one), would I feel I was meeting my legal (and insurance) obligations if I accepted a Nitrox card as proof of any kind of other certification? No.
You feel free to make whatever assumptions you want about what other C cards a person has based on seeing a Nitrox card. As I said in the beginning, I would never assume that anyone would take my Nitrox card (or any other C card that doesn't require any dives) as proof of any certification to dive. When I go to sign in at a dive operator, I take my AN card and my DP card. The AN card actually does require dives, but I still take the DP card, just to make sure there are no problems.