Auto Insurance Claims: What is going on???, split file, insurance info

Question
About a month ago, I got into a small accident in the alley way of my neighborhood.  It was the other driver's fault because at the intesection of the alley, I saw her car, so I stopped mine, but she didn't see me, and she ran into my car.  When we got out of our car, she did not want to trade insurance info because she said, "our insurance companies can deal with our own cars."  I said, "No, it's your fault because you ran in to my car."  I told her that I wanted to call the cops, but she said, "no, the cops can't do anything."  She was being very difficult, so I finally said, "fine, either you give me your insurance info or we're calling the cops."  So I filed a claim against her insurance, but her adjuster denied it because he said that by the looks of everything you could not tell who was at fault.  I was furious!!  That was three weeks ago, today I got a letter from her insurance company saying that they're going "to investigate the details surrounding the accident.  If the investigation determines that if you are liable for the damages, it is your responsibility to make sure that we are reimbursed for the damages."  And it was signed by the SAME ADJUSTER who said that you can't tell who's fault it was!!  

What is going on?  Did they not investigate this accident before he denied my claim?  I am furious because first they denied my claim, now they want to investigate it again to see if it was my fault?  Should I take this matter into court?  

I live in the state of Texas

Answer
First some questions...

What State?

Who is the other party's insurance company?

Simply because you were stopped in an intersection when struck doesn't automatically make it the other parties fault........

Was the interscetion on public or private property?

Was the intersection controlled by any type of traffic device (signal, signage, etc)?

What were the points of impact on the respective vehicles?

What we appear to have here is a split file... one part of the file is being handled by the other party's LIABILITY team (your claim v their Insured) and the other part is being handled by their MATERIAL DAMAGE (Property Damage) team (the other party's potential claim v you) that handled their Insured's Collision claim and is now looking to recover their payment (the process is called recovery or subrogation)....  it is not unusual to have different people working the same file and at different paces.... that's SPECIALIZATION for you!!!

Get back to me with answers to all my questions and we'll sort this out for you.

Please take the time to rate this prelimiary response in the various catagories...


Thanks