So, to be clear, you place the dough into a Cold dutch oven, which is then placed into a hot oven?

Read the Author’s Note. She clearly says to preheat your Dutch oven IF IT CAN BE HEATED EMPTY. That IF is probably why it’s not included in the recipe directions.

“If you have a Dutch oven or pot that you can preheat empty, do that! You'll get an even better crust on your loaf. But if you can't (and check, not all pots are safe to preheat empty), it'll be deliciously crusty and chewy regardless.“

I think we are all on the same wavelength... Manufacturers of enameled Dutch ovens say to never put a cold (I take that as also room temp) Dutch oven into a hot oven, rather put the empty pot into the cold oven and heat it along with the bigger oven. The recipe I follow for no-knead bread is similar to Jim Lahey's that Nancy mentions, and calls for heating both, then placing the dough, on a sheet of parchment, carefully into the hot Dutch oven and then into the hot oven.

This is interesting because I know that you can bake bread in a cold Dutch oven, starting it in a cold oven. The results are just as good and can be used for other bread recipes, not just no knead. King Arthur Flour tested this method: https://www.kingarthurflour.com/blog/2017/07/05/baking-in-a-cold-dutch-oven

But this recipe has the oven preheating before the end of the last rise, so I'm a little puzzled too.

Lynn - I think you're right to question the recipe.
Below is a link to a feature on originator Jim Lahey and his original recipe.
He heats BOTH the oven (appliance) and the Dutch oven (heavy lidded pan) before adding the risen dough.
Also, he includes the parchment paper as a necessary (not optional element).
Maybe Posie Brien has developed something new.
I've made many loaves of both regular and no-knead bread (though not this recipe). If it were me, I'd make Lahey's version first and/or wait to hear from Posie.
https://www.bloomberg.com/news/articles/2017-03-27/new-york-s-bread-master-teaches-you-how-to-make-easy-sourdough