Every time someone has a casual "Well, you can just sue them" answer to being wronged, they forget that the court system (at least in the US) is inaccessible unless you're rich and richer than your opponent. If my employer does something wrong to me, like wage theft, fraud, harassment, discrimination, it doesn't matter that I can sue them in theory. In practice, it's me and my $5,000 in life savings vs. 100 corporate attorneys working at a $N billion company who will inundate you with paperwork and motions and procedural tricks. Not to mention, if you sue them, they will fire you in retaliation (which is also probably illegal) and may even go so far as informally blacklisting you in your industry. So you're giving up your time, your life savings, likely going into debt, and giving up your future employability, just to pit your one already over-worked attorney vs. their army. Good luck.
That doesn't mean that suing is easy or cheap, but only that things are way more balanced than your comment makes it look like.
One attorney may be all you need if the evidence is grossly in your favor. No point denying yourself the opportunity, especially if you can afford the consultation fees.
If its a difficult case, then a good lawyer will tell you ahead of time that they don't think they can win and that you probably shouldn't pursue the case. If its borderline, they'll probably accept the case but you gotta pay them.
If its ridiculously easy, they'll take the case for free on their dime / contingency (because they're so confident they're gonna win).
Vis a vi the original question,
"I never said that. Do you have a recording?"
Especially when you get the follow up questions, and find out HR left contemporaneous notes in their HRIS tool, which corroborate the story.
Remember that the standard for a civil suit is not “beyond a reasonable doubt”, but “more likely than not”. I really don’t think you’d need a recording to win that case.
Employees with grievances sue companies all the time, because it works for them.
Companies may have lots of money, but that doesn't mean they want to burn it. They'll often settle even frivolous lawsuits because it is cheaper than litigating.
On "slam dunk" cases, some lawyers will work for small retainer and large cut of settlement. You no longer have to spend time chasing. You just supply lawyer with info when requested.
In a case like this, your lawyer would send their lawyer a letter, their lawyer would tell them they’re going to lose, and you’d negotiate a settlement.