Having read all the posts on here for this situation, (yes), I am one of those morally responsible people (I even go back into the store if the cashier gives me too much change ... that's just me ... been that way all my life ... long story).... but... to get back to the original topic ...
I think the driver of the vehicle should turn the claim into HIS insurance company first. If the insurance pays ... all is well. If the insurance company does not pay ... suck it up! NOW, make a claim with the trailer's owner's insurance company. If they pay ... all is well. If they don't ... then you both split the difference.
Will your insurance rates increase if you make a claim? I don't know? That depends upon your past driving history, previous claims, and the type of policy you have. But the RIGHT thing is for the driver to try first. Regardless of having a spotter or not, it was the driver in control of the vehicle, and in the end, it was the driver who made the decision to move forward ... which caused the accident.
Or, you could just skip the whole thing, and pay out of pocket for the repair. (personally, this is what I would probably do, as my insurance rate would probably increase if I made a claim.)