This is outright stupid to believe. I have been working for past 15yrs and worked across startups to Top 5(FAANG), and never seen or gone through this.
Happens in consulting more often than you think. Product firms run different or at least that's what I assume. I haven't worked in FAANG but have worked in the Big4s, and a couple of Fortune 50 manufacturing firms. The experience I talk of has to do with the Big4.
In all seriousness they mentioned India not mango fango. That said, my xp has been the same as you. Only time top performers get nixed is if a whole arm gets nixed and they get caught in the crossfire.
OP said "do well", not top performer. Thinking you're a top performer isn't the same as the company thinking you're a top performer. I've never seen someone put on a PIP that didn't deserve, even if they thought differently.
Most people struggle just to keep their head above water nonetheless come up with elaborate conspiracies of sabotaging other peoples careers. No one is thinking about you that much.
I suspect the root of the problem is an unwillingness to take ownership for their action (or inaction). I've never been on a PIP. Even when I've given my employers reason to give me a verbal warning, their response has been: "that's not like you, don't let it happen again," and it hasn't happened again. I suspect that is true for most of those who have never been on a PIP.
Now I'm on the flip side, in a place where I may have to put someone on a PIP. What can be done has been done. There is only so much support and positive guidance that can be offered before you have to provide them with a plan backed with consequences for not following through. It is an employee that I don't want to lose because of their contributions, but it is also an employee that I can't afford to keep because (without changes) they are a liability. Unfortunately, previous interactions suggest that I will have to cut my losses. Yet the ball lies entirely in their court at this point because they are the one who has to take ownership for the issues they create.