The chicken fat layer in the skin is flammable. As it melts, it drips out and down. If there is something extremely hot underneath it (like hot charcoal), it will ignite causing a flareup. Heat rises, so the heat and flame go back upwards to heat the chicken more, causing more fat to melt and drip. It is a self-reinforcing cycle.
To prevent the cycle from beginning:
- lower the heat level
- put a drip pan between heat and the chicken
- move the chicken so it isn't directly above the heat
- start with the side of the chicken with skin facing down, finish with it facing up
If you actually get the skin hot enough to catch fire while on the chicken, you're REALLY using too much heat.
I suspect you may have created a poor-man's slow-cooking environment in there. You had meat, and liquid, and a median temperature of around 200° F, and you probably also got the bird close to "done" during the first broil, before you even left the house. This is obviously easier to do when the meat is covered (was it in a covered roasting pan?) due to the steam, but the oven does provide some insulation to begin with.
Technically when slow-cooking you should theoretically be able to speed up the process by quickly bringing the meat up to just below doneness/moisture-loss temperature (130° F) and then switching to a moisture-preserving slow-cook method like braising. I think that's what you accidentally did, but it's hard to say for because nobody was there for an hour and it sounds like you didn't check the temperature before the second round in the oven.
My guess is that the second roast at 400° F was probably unnecessary, and that the bird was already done, having been cooked in a very slow roast.
I'm pretty sure it wasn't the basting that helped. It seems to be regarded as a myth these days that basting keeps the meat moist, because the baste really doesn't penetrate the skin (and it's not the skin you're worried about). Basting is done to add flavour, not preserve moisture.
The recipe itself also doesn't strike me as anything special in terms of keeping the bird moist, aside from having a relatively short cooking time (as with any grilling/broiling) and letting the meat rest afterward, neither of which really apply in your case. It was probably the slow heat that did it.
Best Answer
I provided this answer a couple of years ago for a similar (but not a dup) question: https://cooking.stackexchange.com/a/25668/6279
Soak cheesecloth in melted butter and drape it over the bird prior to putting it in the oven to roast slowly. This will capture the juices making your chicken moist. 30 minutes (or so) prior to finishing remove the cheesecloth and return the bird to the oven to reach that golden color. The butter will help crisp up the skin as well.
I would recommend an oven temp of 275°F (135°C) until the internal temperature of the breast is @145°F (63°C) and allowing it to reach 165°F(74°C) after the cheesecloth has been removed. An important part of this is to use internal temperature as your gauge to when it is done. If you simply watch the clock you may get lucky, but your results won't be consistent.