Well, there are "Standards of Fault" from case law, that are used to determine fault. And if the other guy was going straight through the intersection, and you were turning . . .. you should have yielded to the oncoming vehicle - legal turn or not - which DOES make you mostly at fault for the accident. It's actually kinda generous of them to declare their guy 20% at fault - they didn't HAVE to do that.
Now, this is lesson learned for next time, of course, but when you don't have collision, even if you think the other guy is at fault, have your car towed to YOUR HOUSE. That way there aren't any storage fees - just the towing bill.
NONE of this is Travelers fault. THEY didn't hit you. The other driver did - when you turned in front of them. You're right - it took WAY too long for them to look at your car, BUT, you're not their policyholder! THey have NO obligation to you, until a judge says their guy is at fault and has to pay!
Now, I know you're not going to pick me for best answer, because you're not going to like these things. But next time, if you want YOUR insurance company to help you work a claim, you'll have to buy the collision coverage. And before you turn left into an oncoming vehicle, be certain they aren't close enough to hit you, even if they floor the gas. Because now YOUR liability will likely be paying 80% of THEIR damages, and 80% of THEIR medical/bodily injury.
Actually, if you REALLY think they're 100% at fault, just call your agent, and ask them to call your adjuster (because you KNOW they're going to go after you for the 80% of damage to their car), and ask if your insurance company agrees with their determination of fault. See how much your liability ends up paying out - and ask them for the percentage.
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