I've been in a similar situation as that described by the author, and went shopping for lawyers.
The four lawyers who would even talk to me basically said this:
Even if you have documentation, there's nothing stopping a company from producing an "HR file" that shows they tried to correct an employee's course, and the employee failed to meet expectations.
There are laws in some states where, if you ask, a company is required to send you all documentation they have about your employment. So I did, and was shocked at how out of sync their records were with reality.
What their records showed was a belligerent, reluctant, and untalented employee, one who was given many many warnings.
Which is not what my actual experience. I was routinely praised by my manager for exceeding expectations, had great relationships with everyone I worked with, could prove that my contributions made the company 3x more than they paid me, etc, etc.
But when struck with pancreatitis, they let me go. While I was in the hospital. Their reason: I didn't request the time off. As if that's a thing you do when you nearly die and are saved by emergency surgery.
TL;DR - it's easy to say "lawyer up", but in reality, much harder to fight than you think, even when you lawyer up.
The good news is I work for a company that doesn't just encourage people to use unlimited PTO, they will frequently pay for vacations for people who go above and beyond. Like, 5 star resort, airfare included for 10 days for up to 4 people.
When my dad was diagnosed with cancer, they said "do what you need to do", as I was his only caregiver. Feeling a bit cautious given past experiences I went on FMLA so that, should things go bad, at least I'd taken the correct legal steps. After being away for two months, when I got back they said "we have unlimited PTO, so we let you use 5 days of FMLA just so it's official, but paid the rest. Welcome back." So, in a way, the first company described did me a favor, since I wouldn't be at my current company had they not fired me.