I don't think the other insurance company can write off your vehicle, but since they have changed you title already your insurance company may now want the salvage title inspection. At this point I would be talking to a lawer and see if you have any options. Have you talked to the other guys insurance company?
Would they have written off the other guys car, and this is now a mistake on there part?
Sorry to hear about this happening, and I hate insurance companys.