I saw that episode a few days ago, and he didn’t so much prove that adding oil doesn’t affect the pasta as that it doesn’t go anywhere. He put a measured amount of oil in with a batch of pasta, cooked it, then was able to recover essentially every last drop of oil from the water post-cooking. The inference being that none of the oil is in the pasta.
Adding a splash of oil does help prevent boil-over, at least. Cooking pasta in a properly large pot does just as well, though - I never use anything smaller than an 8-quart stockpot for pasta, filled 2/3 with water, and that’s only because I’ve got something else going on in my 12-quart pot. If you have to keep stirring the stuff, your pot’s too small!
As for rinsing - never. As I saw in a “Cooking for Utter Idiots” type cookbook once, “Your spaghetti just had a nice hot bath. Why would it need a shower?”
My electric stove is old and doesn’t put out as much heat as I would like. When I add the noodles the temperature drops too much, sometimes to a bare simmer. I either have to stir until the noodles stop sticking together so much and the water returns to a good boil, or just add a bit of oil. Yeah it just sits on top, but convection currents carry the noodles up the center, through the oil, and down the sides, so it’s not like the oil is useless.
There is one isolated reason to rinse pasta. My sister-in-law was preparing to cook for the church spaghetti supper. She called the Creamettes company to find out how to make lots of spaghetti ahead of time without having it all stick together before serving. They said, "Rinse it after cooking, and it won’t stick together.
By the way, in the previously mentioned Good Eats® food myths show, Brown says you can keep pasta from sticking by cooking in much more water than most folks use. The starch gets diluted in more water.
If your stove won’t heat water quickly, start with hot water from the tap, so the stove only has to raise the temp by 60 or 70 degrees F.