No truth was told to the OP. You need to document your reasons why a PIP is needed. As someone points out in this thread, the whole point of the PIP process is to get a paper trail ready if Google is going to fire someone to avoid accusations of discrimination. HR will block any PIP with "My manager says so" as the basis.
The people that say "My hand was forced" are lying to you and lying to themselves and are frankly poor managers.
My alternative theory and one that is more common and I'm not sure why it didn't come to me first is OPs manager is conflict avoidant and wants to always be the "good guy". Firing people is no fun. PIPs are no fun. It's the cowards way out to pass the buck.
To put it another way, if OP asked their skip why they are in a PIP, what do you think their answer would be? It'd likely be something like "Go read the PIP document yourself" because they have confidence they have documented underperformance in the PIP tool.
The whole point of having line managers write PIPs together with employees is to have these vaguely valid-seeming reasons on PIPs. There is, however, also a reason the PIP process got initiated. It is never the line manager that initiates a PIP process (you'd have to have exceptionally poor performance for that, frankly I wonder if they even have the power to do so).
You get onto a PIP because some external-to-the-team person, maybe a TPM, maybe a higher up manager, complained about you. They don't always explain why to your manager, in fact, it's probably generally a smart move for them NOT to say why (frankly, some people complain to your manager because you came to the office with untied shoelaces).
When that happens (maybe your manager gives you two or three "strikes"), your manager comes to you and writes a PIP. What that PIP will NEVER say is "make X not complain about you anymore". It will say "write more code", "take ownership of bugs", "take more feedback into account", because, as you point out, HR would freak if it said "do what X says". Plus, of course, if at all possible your manager will try to not have you work with that complaining person anymore. Which would make such a PIP redundant/impossible.
PIPs are always because someone asked for them. Maybe (hopefully) indirectly, and not always (one hopes never, but ...) for the reason "quota", but essentially always because someone asked for them. PIPs never say that, so they never give the real reason. The point is indeed to scare you into being "more cooperative".
HR kind-of tells the truth: the point of a PIP is to make you a better employee. It really is. All else equal, they want it to go away as much as you do. But if it doesn't go away, the point of a PIP is to fire you, safely, without getting sued afterwards, without HR having to do any work at all.
The people that say "My hand was forced" are lying to you and lying to themselves and are frankly poor managers.
My alternative theory and one that is more common and I'm not sure why it didn't come to me first is OPs manager is conflict avoidant and wants to always be the "good guy". Firing people is no fun. PIPs are no fun. It's the cowards way out to pass the buck.
To put it another way, if OP asked their skip why they are in a PIP, what do you think their answer would be? It'd likely be something like "Go read the PIP document yourself" because they have confidence they have documented underperformance in the PIP tool.