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I went back and rewatched it.
LF says, "If one was going to harm the other, wouldn't [Brienne] be bound by honor to intercede?" Sansa replies, "She would."
My interpretation now is this: LF says it as if to imply that Brienne would protect Sansa if Arya tried to harm her. But what he really meant, and the way Sansa takes it, is that the only way to harm Arya is if Brienne isn't around. So Sansa sends Brienne away so that she can be free to kill Arya.
I still think that doesn't make sense, but it's the best I can come up with.
This is my line of thinking on that convo too...