Here's my guesswork for how they generally get used: "at" is for a specific location that could be represented as a point, usually when you're inside or at the edge of it, where it doesn't matter what part of it you're actually at, usually in the context of travel or giving directions. "on" is more for certain things that are large, where you're not trying to be specific, probably when you're literally on top of something or using it. In is when you're literally inside the bounds of something, but again it's relatively unspecific.

You can't use at when a thing has too large of borders. You can't use on when you're not on top of it. You can't use in when the thing doesn't have defined.

But I guess really it's like you've said. The meaning of each preposition is specific to the noun it is paired with.