It has just occurred to me to wonder if we were perhaps a monk in a past life.
There are so *many* possibilities for our Secret Love flaw, after all - and if that were what was going on, this fox spirit would certainly qualify for "desperately in love with you, and will do anything to have you".
Thinking, though... this is a kitsune. Even assuming that what she says is true, she is a trickster spirit, and also constrained in what she may say, and there are many things she has not said. It is *highly* likely that we're not getting the whole story. I think we'd be well-served to approach this (at least initially) as an investigation challenge, rather than a combat challenge.
Fortunately, we have some degree of authority with which to do that. We are a crab samurai, in Crab Clan lands, acting (at least to some degree) under the orders of a well-respected mid-range official in the clan. Additionally, the fox spirit was apparently working on behalf of the clan ("chasing off some interlopers from Gaki-do" generally qualifies as serving Crab Clan interests, at the very least under "harrying and denying succor to the foe"). Also, finding her den and making off with her stuff could very easily be taken as theft. Admittedly, this is all a bit on the thin side, but there are Crane and Scorpion who have made a career out of killing people in duels with less justification. It's at least enough to give us a reason to approach them, declare that we are investigating, and request answers. If their response to official inquiry is to attack or flee, we can give an appropriately vigorous response of our own without further concern. If it's anything else, we can find out more about the situation before acting.
[x] Approach the Ronin camp.
[x] Hail the guard, if there is any. If there is not, rouse one of the ronin (probably with our testubo - nudging rather than attacking). Inform them that we are Hiruma Sousuke, here on the business of the Crab Clan (for cultivating potential allies against Gaki-do *always* qualifies as the business of the Crab Clan) and that we wish to speak with their leader.
[x] Inform the leader that a Nemuranai (describe the necklace) has been stolen recently, that we and our men have been assigned to retrieve it, and that by speaking with the spirits, we have determined that it lies somewhere within the bounds of the camp. Ask that the ronin leader please provide the nemuranai, as we would not wish to have to charge them with possession of stolen goods.
Worth noting that every word of the above is true. (the bit where we state that it's a nemuranai is a reasonable assumption, based on the fact that it's made of jade and the fox spirit stated she could use it to find her lost love on reincarnation) There is no reason to sully our lips with lies.
It also implies that we've been assigned this as a mission by crab clan higher-ups, that we either are a shugenja or had shugenja support for it, and that by extension whoever it was stolen from is Pretty Darn Important Indeed. If they challenge us based on where they find the thing, we can reveal that, yes, it was indeed stolen from a Kitsune, and ask if they have a point to make. If they challenge us on anything else... well, then they are telling us to our face that we are lying... and in Rokugan, when your social inferiors tell you to your face that you are lying, you have all *sorts* of appropriate responses. They're unlikely to do that unless they want a fight to the death.
edit: looks like you could actually concatenate
@EtchedSteel's vote and mine. That's cool.
I will note that the kitsune specifically said that there wasn't anything in the rules against two humans talking about their interactions with her. We can pretty much tell the ashigaru whatever we want, and have it be okay.