EMC Insurance EMC Refuses to Pay Claim - Acknowledged Other Party at Fault, but Stated Other Insurance Doesn't Want to Pay so I have to

I was in an auto accident on October 4, 2017 in which the other party was at fault. Office Jones responded to the accident call and the other party provided both a verbal and written statement that I was driving straight on a main street and that she pulled out of a parking lot, turning left, and hit me. I collaborated both verbally and in writing. Today is November 1, 2017. I have made numerous calls to the claims adjuster and to my agent and they are refusing to pay my repairs of $779. I have been repeatedly informed that the responsible party's insurance (Progressive) doesn't want to pay, so I am responsible for paying my $500 deductible, even though the other party admitted fault. EMC has provided the worst insurance customer service that I have ever experienced.