I also think that the frame story is far more primitive and lacks the depth of Boccaccio's frame story, but because The Canterbury Tales is an unfinished work, it's unclear if Chaucer meant to at some point tie things in tighter or cross reference more.

I actually think that I could go farther on the Filomena-Fiammetta conflict if I could prove that Filomena is the one whom Boccaccio mentions as being a Ghibelline. I say this because Fiammetta's story on Day 10 (X, 6) begins with a statement of how good it was that the Ghibellines were driven from power, and Boccaccio says that "alcuna, chi quivi era Ghibellina, commendar nol volesse" (a certain girl who was a Ghibelline there did not want to commend the story). This leads Pampinea to tell a pro-Ghibelline story (X, 7), after which Boccaccio states:

Filomena, per comandamento del re, essendo Pampinea di parlar ristata e già avendo ciascuna commendato il re Pietro, e più la ghibellina che l'altre, incominciò:

(Filomena, by order of the king, as Pampinea was finished speaking and each one had commended King Pietro, and the Ghibelline more than the others, began: )

This could simply mean that the girl who is the Ghibelline approved of Pampinea's story more than the others because it followed an anti-Ghibelline story and was itself pro-Ghibelline. Indeed, I have seen the Ghibelline identified as one of the other girls (I forget which one) based on conjecture. However, the fact that the statement immediately precedes Filomena's story and is set into a sentence starting with "Filomena" and ending with the verb she is the subject of, it might be a hint that she is the Ghibelline. In fact, you could try to translate the sentence as "Filomena, by order of the king, as Pampinea was finished speaking and each one had commended King Pietro, and more the Ghibelline than the others, began:", in which case the meaning could be double-edged (i.e., Boccaccio isn't just saying that the Ghibelline is happier, but is saying Filomena is more of a Ghibelline than the others).

If that is the case, then Fiammetta's story on Day 10 is told as something of an attack on Filomena, and Pampinea (as the de facto leader of the women) steps in to avoid a catfight, so to speak, over Filostrato.

However, because I can't really prove that Filomena is a Ghibelline, that element is sort of on shaky ground so I didn't want to put it in the main review.