Let me start by saying, that anytime someone rear ends you, the insurance always pays at 100%. The reason being is the following reasons:
-not paying attention
-following too closely
-not keeping an assured distance.
As a (former) auto adjuster that handled auto claims for 10 years with many companies, there was only (1) instance we paid 50% vs 100%, and that was because our policyholder claimed that the other driver had no brake lights and stopped, not at a light or stop sign, but out of nowhere. When the officer came to the scene, he told the officer, who validated that the guy did in fact had no brake lights and noted on the police report. But, that was only 1 exception, of maybe 500 claims or so, that we paid, or the other insurance paid at 100%.
People stop all the time, be it for a pedestrian, a kid, an animal or something on the road, thus the following reasons I listed above, usually applies, thus rear ending someone.
I agree with others, that if it is too dusty, and he could not see, he should have had his flashers on, drive slower, or even pull over to the side/ditch to let the dirt/dust clear, but, most country roads I have been on, will have signs up warning of approaching a stop sign, so he should have anticipated slowing, or looking for that stop sign, to stop. For an adjuster to state, you should not have stopped, or it was too dusty, is probably one of the stupidest reason I have heard for an adjuster to deny a claim. Did you actually get a letter to from them denying due to this reason?
Do you have collision coverage on your policy? If so, then have your insurance pay and go after them for payment. If, only liability, then if damages less than $5,000, you can sue him in small claims court and do not need a lawyer. You DO NOT sue his insurance, you sue him, since his insurance did not rear end you, he did.
There is no judge out there, that will buy this crap of the dust, so have your insurance, or sue him in court for your damages.
good luck