"Unsuspecting coincidence is a known fact"
Yes, the word coincidence exists because coincidences occur. Coincidences are relatively rare and can be very remarkable, but they're not impossible or miraculous.
In fact, if we lived in a world where coincidences never occurred, that would be something far more remarkable and incredible as it would represent a seemingly selective suspension of the mathematical laws of probability.
It's important to note too that coincidences and seemingly rare occurrences often seem rare because of our own ability as humans to attach meaning and see patterns in events. To illustrate what I mean by that consider the following:
What are the odds that I will achieve the following sequence of numbers if I rolled a 6-sided die 11 times: 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6 ? the odds are 1/6 to the power of 11; or 1 in 362,797,056. That seems like a very rare event doesn't it? One might even argue that it is unlikely that you'd get that specific sequence of numbers if you kept rolling the die constantly in sequences of 11 for 10 years!
Now here is the kicker: take the same die and roll it 11 times and record the sequence you get. Do you know what is the odds of getting that particular sequence - in fact any sequence of 11 numbers? It's 1/6 to the power of 11; or 1 in 362,797,056 - the exact same probability as the "special" symmetrical sequence mentioned above! Yes. Every time you roll a die 11 times the particular number that comes up is always a very rare event having a probability of 1 in 362,797,056!
But because our brain is wired to look for patterns and because we have ascribed the significance of order and symmetry to the first pattern, and because we are looking to get a preconfigured pattern, getting the first pattern would seem incredible. And yet, every other pattern that we get is just as unlikely, just as fortuitous, but we disregard them because they have no special significance to us . . . unless we get 362,797,056 volunteers to engage in a lottery-like game where each one writes down a different one of the unique 11-digit patterns corresponding to each of the 362,797,056 numeric combinations that can result from rolling the die 11 times in succession. Someone is bound to win!