You've just described "individuals and interactions over processes and procedures".
The agile manifesto isn't the cluster fuck that Agile has become. Agile methodologies directly violate the agile philosophy, but that's no reason to pretend that we're just now discovering that methodologies suck. It's in the manifesto.
The difficult part of being a good PM in a team is that Agile is hard to do right with real humans. Even if it can be reduced to the Agile Manifesto, putting it in practice is difficult and takes work, time, and skill. The ability to consistently create good practices are what differentiates the good from bad PMs.
So while I agree with you that it does reduce to the Agile Manifesto, I'd also say that from a PM's perspective, that's not the point.
