Thus throwing out EVERY piece of knowledge. There is no such thing as 100% sure. That just isn't how the mathematics works.
The way to avoid this issue is to AGREE BEFOREHAND which way the cue ball will go on a good hit, and where it will go on a bad hit. Then there is no argument afterwards when people might be biased about the result.
Nothing to do with math, "100% sure" in this context is an opinion. Not a mathematical proof.
The opinion can actually be wrong -
I can be 100% sure I saw a good hit when in fact it was a foul.
But the point is, if there's uncertainty, you give it to the shooter.
If you have a "piece of knowledge" that makes you 100% positive you saw a foul, call it.
If you have a "piece of knowledge" that makes it
likely you saw a foul,
but you aren't willing to say "I'm absolutely positive that's a foul" then you can't call it.
(or you can try, but expect some debate)
Agreeing beforehand is a good idea if the shot allows for it.
Some situations are no-brainers ("if the six ball moves at all it's a foul")
Other situations, like split hits, don't allow for this.
Like here, both balls are going the same direction whether it's a good hit or not.