I agree with your first paragraph, but my experience with the second is that I’ve always been offered it at that figure. (The insurance company is negotiating with you to buy the car from you. They may not want to present it in those terms, but that’s what’s going on. You own it; they have an obligation to you; in some cases, it’s advantageous to all sides for the insurance company to buy the wreckage from you. If they think they can get $X for salvage, it’s cheaper and easier to offer it to you for that; it ends storage fees, avoids transport and selling costs, and in most states avoids them paying sales tax to you on the salvage amount.)

Go one step further with the car, you salvage the car, they say it’s worth $100, does the insurance company have to sell it to me if I offer $101?

Of course not. That’s implied by my agreement with GP’s first paragraph.

Whoever owns private property decides its disposition. Depending on what you mean by “you salvage the car”, either the car was never owned by the insurance (in which case they obviously can’t sell it for any price) or it is owned by them (in which case they still don’t have to sell their private property at all, nor to a $1 over-bidder, and not necessarily to the highest bidder).

The company's officers are obligated to be fiscally responsible. If they won't accept half a million dollars for something with negligible value, they're not being responsible.

The thing is that they claim it's value is X to the Tax Man.

Then someone says "I want to pay 1.1 * X for that" and they say "it's worth more" - what are the tax implications?

The same applies when they claim that X = 0. They're doing a disservice to their shareholders if they won't sell something worthless for money.

There's a celebrity president facing the courts for a similar play, the same thing was worthless when having to pay taxes for it and priceless when using it as collateral for a loan =)

Someone is saying "the way this works is wrong, it should work differently" and you're responding "that's not how this works" to that. How does that help?