They know they are going to settle for some amount but that is their tactic to keep that amount down while you, of course, are trying to get that amount maximized?

I'm in sales and I do a lot of negotiating, I'm pretty good at it, and some of the tactics many guys use are similar, offer less ask for more depending on which side of the table you're sitting. Also Insurance companies refuse to pay the amounts medical providers bill all of the time, it is part of that game. An FYI my wife is a medical professional so I'm fairly well versed in these things. But insurance companies reject bills all of the time for being "to high" and will only pay certain amounts for certain procedures or types of care. Medical professionals that accept insurance know this, they have negotiated this stuff up front and know what an insurance company will pay and overbill purposely. I can certainly see where a lawyer can be helpful in guarantying that the client cannot be pursued because the insurance company will only pay a set amount.