I feel like saying Gambler's Fallacy to someone who knows what R is is borderline aggressive but, out of a maximum of good intentions, the thing you've labeled as an assumption is called the Gambler's Fallacy and it is so named because statistics does not work that way.

https://en.wikipedia.org/wiki/Gambler%27s_fallacy

Consider the case of a fair coin. We agree that, if one flips a sufficient number of coins 100 times, eventually one of them will come up with 100 heads, right? Pretend you've got a factory in China filled with people flipping fair coins until one station shouts out "GOT IT!"

Do you think that there's some property that the universe attaches to that coin which makes it more likely to be heads, or more likely to be tails, simply because it "feels" anomalous if one happened to be flipping only that coin and not one of the thousands being flipped simultaneously in the factory?

No, that's preposterous. The universe doesn't care what feels anomalous to us. It's a fair coin. The next shot is like every other shot: 50/50.