Peter/Mark of Papias versus Peter/Glaucias of Basilides

The testimony of Papias that the Gospel of Mark was written by Mark out of Peter’s anecdotes is recorded by Eusebius (HE 3.39.15):

And the elder used to say this: ‘Mark, having become Peter’s interpreter, wrote down accurately everything he remembered, though not in order, of the things either said or done by Christ. For he neither heard the Lord nor followed him, but afterwards, as I said, followed Peter, who adapted his teachings as needed but had no intention of giving an ordered account of the Lord’s sayings. Consequently Mark did nothing wrong in writing down some things as he remembered them, for he made it his one concern not to omit anything that he heard or take any false statement in them’ (trans. M. Holmes).

Some argue (e.g., Joel Marcus, Mark 1-8, 23) that the appeal to Mark as the interpreter of Peter is a deliberate rejoinder to the claim by some Gnostic figures that Basilides was taught by Glaucias the interpreter of Peter (Clement, Strom. 7.106). However, I would point out: (a) Imitation is a great means of admiration, but hardly an effective form of refutation. (b) The Peter-Glaucias tradition itself may have been influenced by the Peter-Mark tradition rather than vice-versa. As Birger A. Pearson (‘Basilides the Gnostic’, in A Companion to Second-Centry Christian ‘Heretics’, eds. A. Marjanen and P. Luomanen Leiden: Brill, 2005, 4) writes: ‘The Peter-Glaukias tradition (whoever Glaukias was) can possibly be seen as a Basilidian counter to the Peter-Mark tradition current in Alexandrian ecclesiastical circles’. (c) The aetiological stories of the genetic relationship between ‘heretics’ recorded by the Heresiologists are chiefly polemical rather than historical (though this should be assessed case by case). (d) Irenaeus connects Basilides with a different Gnostic genealogy that is traced through Simon Magus and Menander (Adv. Haer. 1.24.3-7), while the Basilidians themselves laid claim to the teachings of the apostle Matthias (Clement, Strom. 7.108; Hippolytus, Haer. 7.20.1). So I doubt that the Peter-Mark tradition was derived (or contrived) as a response to the Peter-Glaucias tradition found in Basilidian circles.

Papias and the Synoptic Problem

I am currently reading (like everyone else in the blogosphere Bauckham's Jesus and the Eyewitnesses) and I was intrigued by his remark where he intimates the possibility that Papias might be the earliest possible reference to Marcan priority or at least Matthean dependence on Mark:

Mark having become the interpreter of Peter, wrote down accurately whatsoever he remembered. It was not, however, in exact order that he related the sayings or deeds of Christ. For he neither heard the Lord nor accompanied Him. But afterwards, as I said, he accompanied Peter, who accommodated his instructions to the necessities [of his hearers], but with no intention of giving a regular narrative of the Lord's sayings. Wherefore Mark made no mistake in thus writing some things as he remembered them. For of one thing he took especial care, not to omit anything he had heard, and not to put anything fictitious into the statements . . . Matthew put together the oracles [of the Lord] in the Hebrew language, and each one interpreted them as best he could.

Does "interpreted them" refer to the words of Jesus or does it refer to interpretation of Peter's account of Jesus' words as contained in Mark? I wouldn't bet my house on it, but it is thought provoking.