I’ll start with my own anecdotal experience: I’ve never had the timing of adding the oil make any difference as to whether the food sticks. First, let’s look at what this age-old and oft-repeated cooking tip is saying. We are being told that if we heat up a dry pan first, until it is very hot, and then add the cold oil (meaning room temperature, presumably), before we put the food in, the food will not stick. So, the tip does not have to do with the oil and pan being hot, but with the timing of the oil placement being important.
Now, I want you to think very hard. Whether you put the oil in at the beginning, while the pan is cold, and let it heat up along with the pan, or put it in at the end so that the oil gets hot very quickly, the result is still a hot pan with hot oil. Can you think of some scientific or maybe magical, thing that might happen to the physical properties of the pan and oil because you waited to put the oil in? No? Me, neither.
Wait. Mr. Wizard just walked in and told me it had to do with the Leidenfrost effect. You remember when the Mythbusters protected their hands from being burned by boiling oil by first placing their hand in cold water? Yep, that effect. So, this grasping at straws theory says that if you heat the pan sufficiently, the oil in contact with the pan instantly vaporizes and creates this sort of oil slick barrier, so that the piece of chicken, for instance, never comes in contact with the pan, and therefore can’t stick to it. There is this protective layer of vapor between the pan and the oil, and the meat sits on top of the oil.
Let’s say we’re using vegetable oil. Even supposing you instantly get the oil up to vaporization temperature, somewhere between 450° and 500°F, what do you think is going to happen once that meat comes into contact with the oil? The oil is going to immediately cool to a point below its vaporization point. Any layer of vapor that would cause the oil to dance around on the pan will be gone in a jiffy, and if the meat is going to stick, it’s going to stick. And, if the Mythbusters had left their hand in that boiling oil too long, they’d have been severely bummed out. By the way, the combustion point of vegetable oil, or the autoignition point, is 685°F or higher, sometimes much higher. You’d have to seriously over-heat a pan to cause the oil to spontaneously ignite.
The fact is that the idea that when you add the oil has something to do with whether food (especially protein foods) stick, is an old-wives tale and there is nothing but anecdotal evidence to back it up. Making sure your oil is hot enough is a very important part of keeping food from sticking, although not a guarantee by any means. However, what matters is that both the pan and oil is hot, not when you add the oil. For a more thorough article on the need to preheat oil see Serious Eats for Do I Need To Preheat My Oil?