I thought, as a practical matter, it's on the person alleging slander or libel to prove falsehood?

I think sometimes folks don't properly threat model what can be done if someone chooses to think about what the consequences for breaking a rule are and letting that guide their actions, rather than striving to avoid breaking them out of some kind of moral principle.

Hypothetically, if I said "firefax murdered an underage prostitute and then sexually violated the underage prostitute's corpse in 2018 and was never caught, I witnessed it happen and tried to report it but the police refused to even open an investigation, firefax is a dangerous predator and should not be trusted", and you lost your job because of that, should you be the one with the burden to prove that never happened?

It’s complicated in the US. The rules of thumb as I understand them are:

1) The truth is an absolute defense against libel claims, but it is a defense, so you must prove the truth of your claims.

2) Statements of opinion (or that a “reasonable person” would understand to be opinion) are with few exceptions protected. “Firefax is a rapist” is likely to not be considered a statement of opinion. “Firefax is a creepy asshole” likely is. “Firefax is a sexual predator” is probably going to be in a grey area and context and damages will be relevant.

3) The more “public” of a person you are, the harder it is to win a libel case, even the statements were false. For example, let’s say it turns out both that there is some “Epstein List” describing clients and their activities, and also that it turns out Trump doesn’t appear anywhere in that list. Trump is such a public figure (both as a celebrity and as the POTUS) that he would be extremely unlikely to win any libel cases against the internet randos confidently asserting he’s on the list even though that statement would have been a statement of fact, and would have been false.

4) A key part of the “opinion” grey area is whether you imply knowledge of heretofore unknown facts, or your relying on publicly available data. Internet randos might not lose a case, but someone like Elon Musk might if they said something like “I’ve seen the case files, Trump is definitely on that list and has done some sick things”. This is because Musk could reasonably be believed to have had privileged access to the information in question and have non-public facts they are basing their statements on. Internet randos on the other hand are largely going to be considered making their statements on the back of publicly known facts (e.g. photos, business connections, public actions and statements) and general “vibes”