But this success is complete measured through comparison with other players' effort, which is PvP.
PvP is the category PP falls under, there's just no way to use sophistry to twist around that.
I can claim exactly the same as you. Show me one direct effect PvP has on PP. Just because players care about the outcome, doesn't turn PP into a PvP feature. The entire mechanism of PP can and does turn without any input from PvP. Widening the definition of PvP to construct some PvP facet of PP is done entirely so that the PvP'ers have an rallying cry. PP as a PvP feature is a reach at best.