Well, I don't think it would be a stretch to assume that Chico could blame Big Boss for what happened to him and Paz. Plus, we know Chico and Skull Face had some sort of established relationship in GZ, twisted as it was. The age would pretty much fit, and who better to send in to kill Big Boss than his former soldier whom he abandoned?
Hmm... Interesting.
While I obviously like the story, one thing that could've been clearer is Quiet's backstory. She says "vengeance drove me to them." I think this suggests something before Big Boss that led her to Skull Face. But we don't know what it is.
We know part of her wanted revenge against BB, but the way it's presented in the game, that's after he torched her. And she'd be a pretty hypocritical person to hold a grudge against BB for attacking her
out of self-defense. But the game does confirm she was mad at him.
But what does she mean by "vengeance drove me to them." She was already -with- them. She was already working for XOF. I think she's referring to something before Big Boss and Skull Face. I think she's referring to another quest for revenge, separate from BB, and prior to Skull Face, which led her to Skull Face.
So yeah, I'd be more satisfied with the idea you're suggesting. Anything that would perhaps explain how she became a cold-blooded assassin doing horrible things for a horrible person.
Quiet's departure is otherwise quite touching and effective. It's just that bit that puzzles me.