The lawyer you have contacted will be able to explain the Texas laws better than we can and will be able to advise you if you have a case against the insurance company or not. Your legal council will then tell you if you have fighting chance with recovering more from the insurance company or not.

It appears TX procedures require that a motorist needs to have "proper lookout", meaning that they carefully and intelligently observe traffic and understand the general situation of all vehicles in the area of their car. Using this proper lookout information, the driver should then take steps to guard against an accident. Failure to observe the proper lookout standard could be construed as negligence.

If the insurance company is finding you partly at fault or negligent then they must be doing so in regards to this proper lookout standard or a comparative fault guideline. Typically in states that allow negligence or fault laws, if you are found even partially at fault insurance companies can reduce the settlement amount by the percentage they find you to be at fault. To find out if the insurance company is handling this correctly you can contact the Texas Department of Insurance.