They may just be throwing drier than you throw, or forty years of experience gives them a leg up on this activity. In my experience the wettest place on the pot is at the top; particularly when you are collaring in the top as lubrication is required for success. Try using slip from your throwing to lubricate instead of water. It is slick, stays on the surface, and doesn't wet the pot as much.
Here's what I do after I have closed up the pot. I first clean all the slurry off the outside of the pot, then make the "groove" where i want it. I keep a heat gun next to my wheel. When the "groove" is set in how I want it, I turn on the heat gun and direct the air to that location while the pot rotates slowly on the wheel. It doesn't take too long to firm up that area. I will dry the rest of the pot some too, so it will be firm for my next step. Then, with the wheel turning slowly, I carefully use my needle tool to cut into the bottom of the groove. Patience here is important, as you want the wheel to spin several rounds as the needle tool cuts the clay and makes it release the top. Once it has cut through, I carefully remove the top and set it aside. I clean up the inside of the pot wall, cutting any clay from the inside without expanding the wall. I carefully pick up the top and compare its outside diameter to the inside diameter of the pot wall to see if the fit needs to be adjusted. I firm up the top of the pot wall with the heat gun, then turn the, now lid, upside down and set it on the wall so I can trim it, dry and clean up its interior, and adjust the fit. It takes me five minutes to do all of this, as I have 11 years experience, not 40 ;-)
The idea is that the lid will sit inside the bottom pot wall. I use this technique in making animal figure treat jars (see example in attached picture), as well as other lidded forms. It takes making a few before it starts to get easier.