That's the shop owner's opinion, and it might be exactly what he would expect of his DMs.That's what I thought, too. And I still believe you are correct. But, I was doing classroom training for my Divemaster cert a little over a month ago. I asked this question in the class and the shop owner (who is an instructor for PADI, SDI, and SSI, at least) said that as a DM I should treat OW as a certified limit of 60', and AOW as 100'. In other words, if I am working as a DM on a dive excursion, I should not allow anyone to go on a dive that is beyond their certified limits, where I take those numbers as the certification limits.
So, in theory, I am not supposed to let anyone come on a dive that is planned for deeper than 100' unless they have at least the full Deep Specialty. I asked "what about the crusty old diver who's been way past 100' a thousand times, but they only have an OW card?" I was told that it does not matter - i.e. it doesn't matter to the insurance company or the court. Pointing to experience is no protection against a claim that I let someone dive beyond their certified limits.
So, for the OP, the point is that an OW card may certify you to do any recreational sport diving (i.e. to 130') you wish, but if you're diving with a guide or charter operation, they may not see it the same way.
If you are a DM working for a dive operation, your employer is going to make the rules. If you got a job as a DM in Cozumel and insisted on following those rules, your employment status would not last very long.
Furthermore....
I just had a long discussion with PADI headquarters that began with the wording of the rules for wreck penetration and then went to other areas as well. PADI training says that you should dive within the limits of your experience and training. I was quite explicitly told that a diver's experience can allow them to go beyond the specified limits of their certification level--they just have to use good judgment about it.
I said the wording of that was not clear, and I proposed more specific wording for the wreck diving course. I was told that my new wording would be included in the course in the future, and it would be described for diving in general in a future edition of their professional journal.