Hi Norma, thanks a lot for asking this. I've been thinking about dough opening with oil vs flour on and off for the last couple months, and your question led me to think a step deeper. And I'll likely experiment a bit with my pizza as a result.
My first thought when I saw the skin from a distance was "wow, that's shiny and oily". I didn't see an oil container either, though it's hard to say if it was hidden amongst the other items on the counter. The dough ball I purchased had a good amount of oil on it. I'm reminded of the conversation I had with my local pizzeria, that also uses the mesh screen, where he said (and showed me) that the dough ball proofs in the metal container in a pool of oil, or what he called an "oil bath". It's possible that the oil bath is enough where they don't have to add more oil on the counter.
But, at around the 6 second mark you'll see that he adds flour and rubs it in and all over one side of the skin. That side goes over his knuckles, then becomes the bottom of the pizza. My local pizzeria told me they also add a bit of flour when opening too. This is interesting because I've clearly demonstrated that with these screens, oil is sufficient to release the pizza, and flour is not necessary.
What I'm thinking is that they like to add a bit of flour as it soaks up the oil. The result will be an undercrust that isn't oily/fried, but also doesn't have raw flour. Basically the oil and flour offset one-another. I want to try this.
The other interesting thing in watching him open the skin, is at the very end just before he puts it onto the screen, he gives it a stretch right in the center. Usually we think of that as a no-no, but that's because our skins open themselves and would be overstretched. This one gave him full control over the stretch, and the center stretch helped even it out.
Matt,
Thanks for your detailed reply!

I haven't had much of any time to play around with my screens like yours. I think only one bake and the screens still aren't seasoned enough. Just too busy to have time to experiment with those screens.
Matt,
It sounds if you are right if Lucia put their dough balls in oil, that probably that is why the dough was shiny. I remember different times when Frank Giaquinto opened dough balls that were sitting in oil. Frank did add a little oil to the bench though, like in this video. Frank also added flour to the bottom of the dough skin. Can't recall where there was a video of a dough that Frank brought a dough ball that was sitting in a lot of oil, but that pizza crust was the most different than I ever tasted. I had asked Tom Lehmann why that was, but don't know if he missed that post, or if he didn't know why that happened.
Norma