My argument rests on three [currently] observations. The first is what Papias--ahem--"said":
The one narrative feature that distinguishes Gospel of Peter apart from the canonical Gospels (minus Luke 1:1-4 and John 21:24) is that it was seemingly written in a first person perspective:
Even in a Gospel like Matthew, which was written by someone who was a follower and witness to Jesus, doesn't have this feature (instead, Matthew refers to himself in third person).
The tradition Mark being a secretary of sorts for Peter is more applicable to Gospel of Peter than it is to our Mark. Indeed, look what Papias says about it--that Mark, "wrote down accurately everything he remembered, though not in order." Not in order? What is that even supposed to mean? That Mark just copy/pasted a bunch of his notes all higgledy-piggledy? Now look at our Mark. Well, he must be on his way to Munich, 'cause his papers are VERY MUCH IN ORDER. So much in order, it lines up with THREE OTHER TEXTS.
What Papias says about his Mark doesn't make sense with ours, but it does make sense with Gospel of Peter.
My second observation is the parallel of a scene that is only matched between Mark and Gospel of Peter:
In both Mark and Gospel of Peter, it is a single young man, dressed in a splendid/white robe, who greets the women who visit Jesus's tomb, and who tells them that Jesus has risen. They are frightened by this and flee.
This scene is not paralleled by the other Synoptics (including Gospel of the Lord) or John. It is two men who are in Jesus's tomb in Luke, Lord, and John , while Matthew only has an angel arrive when the women do to tell them what has happened. Now this could be paralleled with a scene that occurred before this in Gospel of Peter, where two angels walk out of the tomb with Jesus and the cross at the sight of Roman guards. But that would still leave Mark and Gospel of Peter alone when discussing the women arriving to the tomb.
Observation three.
This one is tenuous, but I figured I'd throw it out. Papias seems to be aware only of a writing by Mark and a writing by Matthew:
Papias never mentions Luke, and despite know "John", never mentions his Gospel either. Indeed, both his Mark and Matthew seem to suffer the same problem of being hard to understand and in an unorganized manner.
But why does this matter? Because Origen and Theodoret make a especial link of Gospel of Peter with that of the Hebrew Gospel:
So a relation between Papias's Mark and Hebrew Matthew, and Gospel of Peter and a "Book of James", and the Nazarenes, who are believed to have used a Gospel similar to Gospel of the Hebrews , is ostensibly but not absolutely made.
So that's my two pennies. Papias cannot have been writing about our texts, and knew of the heretical Gospel of Peter, which he believed was authored by Mark.
I also have a conspiracy theory that the Gospel Cerinthus used/wrote was Gospel of Peter. This is combined with Tim Claason's proposal that Mark and Revelation were at one time used in conjunction of one another, and the heresy claim that Cerinthus authored John and Revelation, even though he supposedly used Gospel of the Hebrews. In short, using the church fathers to reconstruct the canon is like finding a needle in a stack of needles.