The article was a guide to the various chronicles known as belonging to, written by, edited by, derived from or possibly misattributed to Peterborough (Nicholas Karn and Edmund King (and what a perfect name), "The Peterborough Chronicles", pp. 17-29). And Walter of Whittlesey, writing early in the fourteenth story, includes what Karn and King call "the abbey's 'Piers Gaveston story'" (20). Translation is mine, because I am picky:
And in the thirty-fourth year of the reign of that King Edward [I, so c. 1306]... the abbot Godfrey also received at the Borough lord Edward, son of that king, and lord Piers Gaveston, and to these he sent gifts as is here narrated: When the abbot's messenger reached lord Edward with a certain cup to the value of 50 pounds, he asked intemperately ('petiit idem Eduuardus incontinenti') if a gift had also been sent to lord Piers. When the messenger replied that he had not, he disdained the cup and would not receive it: the messenger then seeking out the lord Piers upon the abbot's command bearing a cup valued at 40 pounds, he was granted admission and the abbot's gift was joyfully received with thanks ('gratanter donum abbatis recepit, gratias agens quam facere'). The messenger was also sent on the abbot's behalf as if to beg the advice of lord Piers on the question of whether the other cup would now prove pleasing to the lord Edward, and he replied that it would; the messenger then revealed that he had not wished to receive it, and the lord Piers summoned his chamberlain to say to him, 'Go to the lord Edward and tell him that I would like him to receive the abbot's gift'. Upon their returning to the said lord Edward with the said cup as directed, he received them gladly, bestowing thanks on the abbot ('gratias conferens abbati') for his gifts. 
But the thing is, this isn't a Piers Gaveston story - it's an Edward story. It isn't Gaveston's behaviour that's the problem here, but that of the future king. Not only does he insist on putting Gaveston on a similar status to himself, as a guest in his own right rather than part of the future king's train, but he sends the Abbot - the Abbot of Peterborough, no less - supplicating to an untitled knight for the favour of the prince. The prince who is his guest. Gaveston's reception of his gift actually shows Edward up - he 'gives thanks' to the abbot (using 'agere', which is to the best of my knowledge the usual verb coupled with 'gratias'), and even has an adverb to emphasise his gratitude, while Edward, when he gets around to deigning to accept the gift, seems to give his thanks as a favour ('conferre'). The difference in Walter's word choice there could be due to the difference in their rank, but given the exasperation (and, I think, glee) of the narration, I suspect he's playing the two scenes up in deliberate contrast.
Of course, I understand what Karn and King mean when they call this "Peterborough's 'Piers Gaveston' story" - everyone had one, I'm sure, just as many later had a 'Hugh Despenser' story. He lent himself to flamboyant stories, and Edward certainly wasn't one for being diplomatic about it (although, honestly, Edward, Abbot of Peterborough + host). But Piers Gaveston is never just Piers Gaveston. He's a metaphor for what Edward does wrong - just as the whole sodomy thing in contemporary accounts is never about sodomy, but about the imbalance of power that was perceived to be threatening the entire structure of the state. The abbot is denied access to the prince who is his guest, in stark contrast to the civil visits and interactions with his father narrated immediately before this tale. The abbot is forced to almost double the value of the polite gift-giving he expected on the occasion of a royal visit. The abbot is humiliated, via the messenger, and not only the messenger but the whole monastery are clearly destined to know about it, and probably recount it in gleeful detail. The vividly imagined little scenes, even the snippet of direct speech from Gaveston, savour to me of repeated retellings and scandalised delight.
I'm assuming, on those grounds, that the story is at least a little exaggerated, possibly embellished with details from other similar 'Piers Gaveston stories'. But even in its bare bones, it's interesting, firstly (and most reliably) as witness to the types of stories people were telling and relishing at this point, but also for the hazy glimpse it affords us of the actors within it. Even if only a little of the story is true, Edward is becoming increasingly defensive about people's reactions to Gaveston at this point, and making it worse with his own behaviour. I'd say he's 'acting out' in a teenage way by taking advantage of those times when he's away from his father to enforce his opinion of the proper order of things - and it is completely characteristic of him at this period, to be recognising only in his father any kind of restraint, or constraint, to the extent that he does not feel the need to be bound by usual codes of polite social interaction.
Well, why should he. He's the prince. And people just keep slighting his Piers. They deserve a little tetchiness.
 Karn and King say 100, but Sparke's Latin clearly reads L, not C. They may have silently corrected this in consultation with manuscript sources; but I am translating Sparke's edition. In light of the value of Gaveston's cup, it's not an insignificant question - is the knight worth 4/5 or 2/5 of the prince?
 Walter of Whittlesey's continuation of the Peterborough Chronicle; ed. Joseph Sparke, Historiae Coenobii Burgensis Scriptores Varii, London 1723, 171-72.
 Cf the Latin of the Gloria in the mass - 'Gratias agimus tibi propter magnam propter magnam gloriam tuam'.