The claims adjuster for an insurance company will use a variety of information to determine fault or responsibility in a motor vehicle collision. Part of the insurance adjuster's job is to assess the nature and extent of the damage that the car sustained.
The insurance adjuster normally starts by reviewing the insurance policy and the coverage in effect for the loss to determine what types of damage or injuries are covered.
The claims adjuster next usually contacts everyone involved in the accident. This includes any drivers, passengers, witnesses, etc. The adjuster gets everyone's account of the accident and takes down their statements. If the people involved and or the witnesses have conflicting versions of what occurred in the accident, the liability adjuster may need to conduct in-depth interview with each driver.
The adjuster will also gather and review additional relevant information, such as the police report, applicable state and local traffic laws, and photos of the scene and the vehicles involved.
You asked specifically about the claims adjuster viewing the vehicle. This may or may not be necessary. If the person rear-ended and admitted fault and the damage that you want repaired was to the back bumper of your car then many insurance companies would have you go to repairs shops to get estimates.
The adjuster would then look over the paperwork of the repair shop to make sure their estimate does not include damage to other parts of the car that were not harmed in the accident and to make sure the repairs match up to what their training and experience finds acceptable.
If there is a question to fault and the claims adjuster decides he or she must look at the car then they are usually looking at the point of impact and seeing how it matches up to each driver's account of how the accident occurred. They may also be looking for paint transfer from one car to another in case a person stated that their car did not touch the other persons. Sometimes pictures of the car are all that is needed while other times the adjuster must look at the car in person.
Some insurance companies will have insurance adjusters that will write the auto repair estimate himself or have the company will want one of their "approved" or "certified" body shops to write the estimate. Even if this is done normally you have the choice to use your own repair shop as long as the repair estimate is comparable to the insurance company's preferred mechanic.
If the adjuster does not determine the cost of repairs then a repair shop will do so but the claims adjuster will look over the estimate before permitting the repairs paid for by the insurance provider. To find out specifically about how a company's adjuster will determine fault and/or calculate the cost of repairs to the damaged vehicle speak to the insurance company involved in your claims process.