Because it's shorthand for "the burden of proof is on those making the claim, and negative claims are much harder to prove or disprove." If your rebuttal to my assertion that Taylor Swift is not, in fact a zebra boils down to "you SAY that none of those zebras are secretly Taylor Swift, but maybe that just means Zebra Taylor Swift is just that good," I mean, I can't technically disprove that, but shouldn't the burden of proof be on you?
> negative claims are much harder to prove or disprove.
No, they aren't.
One, disproving a negative claim is exactly proving the opposite (positive, if the same style of expression is used) claim (and vice versa), so it can't be harder to both prove and disprove negative claims, even if they were real distinct classes.
Second, “positive” and “negative” claims are largely phrasing choices; it's quite possible to have positive and negative claims that are semantically equivalent.
If the intention is to talk about burden of proof, then that's what we should be talking about. That's clearly not the case because the parent comment replied asking how it was possible. They seemed to have meant it very literally that negatives are impossible to prove. It's a common saying and it's flatly wrong.
Additionally, in this case, the claim that a company can be trusted is much more difficult to prove than the claim that they cannot be. Burden of proof, difficulty of proof, and whether the claim is expressed as a positive or a negative have no intrinsic link.
_Of course_ it's possible to prove a negative. Why do people insist on repeating this as if it's actually true?