A PIP is an explicit statement of the problems with an employee's current performance and what they need to improve to not be fired. A manager's complaints may be dubious but no more so than they would be if they were outright allowed to fire the person.

I've never heard of a PIP actually succeeding (an employee improving to the satisfaction of their manager) so it delays the inevitable, perhaps allowing the employee to quit and find another job before their fired. It's definitely meant to avoid a wrongful dismissal lawsuit but I think that almost never works; either the employee is going to sue or they're not, "being given a chance to improve" isn't going to change that.