You are probably right... in most cases. Companies have lawyers and those lawyers are very risk adverse. The PIP is basically a period of employment where the company collects evidence on your (lack off) performance. This evidence can be shown as justification for firing, in the unlikely even it is needed.

PIP = "Paid Interview Period"

I've never seen anyone recover from a PIP.

I’ve run several PIPs and haven’t lost anyone. This was in collaboration with a really good HRBP though.