The unforeseeable circumstances of her being there for Robb are not so much, if a bit advanced. Stafford's host was raised in light of Robb holding Riverrun, athwart the Lannisters' lines of communication with their own lands, so their goal was to move east and threaten or attack Robb at some point. Since Tywin would prefer to converge on the Starks with his own force and the new one, an encounter between Robb & Stafford's forces would almost certainly be to the Lannisters' disadvantage, with Jeyne being a good fallback if Robb was getting too powerful.

The only problem with this scenario is it requires a lot more cooperation on her part than seems to have existed in Sybelle Westerling's plot in the books, and is a bit of a risky gamble to ensnare a would-be king, with much greater risks to Jeyne's virtue and whatnot. If she does turn out to be Jeyne, it would be entirely in keeping with the PC tropes I disparaged above for her to have run away to join the army as a medic and "do some good." I confess I had forgotten the specifics of her maternal ancestry which might support her having medical knowledge, as the books made no suggestion Sybelle had passed on her pharmacological expertise (tricking Jeyne into taking contraceptives would be a lot harder, for one thing). Though Jeyne was mentioned tending to the wound Robb took in the attack on the castle, I kind of glossed over that part, assuming it was teenage hormones exaggerating what was nothing more than sitting by his side and holding a cup for him to drink or putting cloths on his forehead and the other stuff people do to pretend they are helping an invalid. In hindsight, she very probably could have had the knowledge and whatnot to provide real treatment.