The debate is over just how "p.p." should be used: whether before the name of the person for whom the document is signed—let's call her The Principal—or before the signature of the person who actually signs the document—let's call him The Agent
The ambiguity arises because "p.p." abbreviates a Latin phrase, per procurationem. It means, literally, "through procuration" -- in English, "by agency", (i.e. "by action of an agent"). However, this bears two different interpretations. You might write (with italics indicating the signature) either
p.p. (by agency of) The Agent
p.p. (by agency for) The Principal
In Latin, there would be no ambiguity, because Latin nouns are declined: they are written with endings which tell you the grammatical case. In the first example, you would write
p.p. Agentis, which is in the genitive case and tells you that it is by agency of The Agent.
In the second example, you would write
p.p. Principali, which is in the dative case and tells you that it is for The Principal.
But English names are not declined, so there's nothing to tell you who is The Agent and who The Principal and which one signed it.
The important thing is to avoid ambiguity; so I would avoid using p.p. at all. There are lots of options out there; here's the one I used when I was office manager at a law firm:
for MyPrincipal, Esq.