Well in general (and not specific to this situation) one of the effective ways you can deal with someone like this is to waste as much of their time as possible in whatever way can. The person on the phone has to have a certain amount of productivity and while they are not going to drop their claim against you if you become a nice pain in the ass they will have the motivation to work with you. If you are quick and easy off the phone they have nothing to loose (their time is preserved).
I've done similar things with both government officials (got a penalty reduced in half) as well as attorneys working on behalf of someone else. Once again you can't be threatening you have to be nice. Waste as much time as you legitimately can is the bottom line.
but aren't you wasting your time too, while wasting theirs? for them, it is a full time job (so they might not care), but for the people who have to deal with them, it isn't
Well you would have to calculate the value of your time vs. either a) cost of attorneys (whose time is very expensive and it's a black box of costs) b) other things that you do that could be offloaded to someone else or perhaps c) putting someone of less value in charge of wasting of time.
We are not talking about hours and hours all at once either. We are talking about being a constant time waster and pain in the ass a little bit at a time or as much as possible while still flying under the radar and appearing not to be doing it on purpose (which you are).
At a certain point people will act in their self interest and perhaps give you what you want. At least that has been my experience when I've followed this path.
I've done similar things with both government officials (got a penalty reduced in half) as well as attorneys working on behalf of someone else. Once again you can't be threatening you have to be nice. Waste as much time as you legitimately can is the bottom line.