If you have comprehensive automobile insurance coverage, I would contact your insurance company immediately and let the two involved insurance companies sort out who is at fault and get your car damage fixed.
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Let your insurance sort it out. If you do not carry collision insurance, write a complaint to the Texas Insurance Commission. On your facts, you CANNOT be at fault.
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Liberty Mutual which is part of Safeco now is getting worse and worse to deal with in my experience. The claims adjuster comes up with ways to find a % fault against you even in clear liability situations like yours.
I agree that if you have collision coverage, go through your own company and let them try to recover your deductible for you. You will be out your deductible initially but ultimately, I 'm sure you'll get your deductible back as well.
The 2 insurance companies will go through intercompany arbitration to decide the issue.
We have seen this before, typically from a low-level property damage ajuster. If you stick by your guns, you may be able to get them to take 100% responsibility. I agree that you should let your insurance company sort it out if possible. It is unlikely that a complaint to the Texas Department of Insurance will do much good, but you should still document what they are doing. You can make a complaint online. I have attached the link.
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