If you could recognize the causal networks behind a complex system the way a toddler can recognize a cat, after being shown very few examples, there would be no need for statistics.
Unfortunately, you can't. (But it doesn't stop lucky guessers thinking they can.)
A scientific hypothesis is correct or not independently of statistical analysis. It's true before it is verified. Statistics is just a social mechanism for demonstrating its correctness to other people (or yourself.)
It's entirely possible for someone to know they're right, actually be right, and it be uncheckable with statistics. The only difference between an outlier and a lucky guesser is knowledge. Blah blah blah anything that's measured ceases to be a good measure blah blah blah.
Per your example, if something has 0 explanation for whatever has 99% of influence, it is just not a useful explanatory mechanism. That doesn't mean there isn't a good explanation.