Hmmm have your guy recover it for free then tell the other company its taken care of. If its an additioal fee that the insurance is not covering then they shouldn't be able to specify who does the work.
Either senerio is not making sense to me though. Not charging for something that cost you money and not having something covered by insurance that is required to be done as part of the covered job. I'd call the insurance company and check it out or look at your policy and make sure it's not covered.