If you watch a pot, will it actually boil?

I’ve always thought I have known what “a watched pot never boils” means.

Like many others, I presumed that a pot only seems to boil more slowly when you pay attention to it, and that the best way to make a pot boil “faster” is to distract yourself with another task or thought.

But, while making lamb stew tonight, it occurred to me that I might be incorrect in my understanding. After all, you can make a pot of water boil faster by putting the lid on it, to conserve heat. Maybe it’s because I’m presently enjoying Wolf Hall, but it occurred to me that there was a time in the not-too-distant past when cooking required wood, and that wood might be scarce or expensive, at least for some people.

If you’re conserving wood or coal, I thought, your cooking fire might keep cool, in a relative sense, by remaining small compared to the pot you were cooking in. It might be that, like a stove on low, the pot’s contents might just barely reach a boil with the lid on. And taking the lid off, to check on it, might lower the temperature below boiling.

Thus, I realized, if you constantly watched this pot, leaving it lidless, it would not boil at all!

Does anyone know more about the origin of the idiom, giving the power to confirm or deny this understanding?