Why are people going to their own insurance company if a wreck is another person's fault and the other person is insured? That's why the other driver is supposed to have insurance.
Being in the industry I can speak directly to this frequently confusing question. Often there are multiple coverages that apply and sometimes it's best to use the other person's insurance and sometimes best to use your own, or possibly a combination of both, just as the original poster, Bocklerider, did. First, let me outline the various coverages for those that might not be as familiar with them -
Coverages that might apply under your own policy -
Collision - This coverage is designed to make you whole after you sustain damage to your covered vehicle - less any applicable deductible you may have. I would note that while most of us have Collision coverage on our own vehicle, it is not required by law. Usually, it is required by one's lienholder if you finance the vehicle.
Med Pay - payments for your out of pocket medical expenses that you incur due to the accident. Often, the amount is capped, depending on the amount of coverage you purchased. This is not a mandatory coverage, so your policy may or may not offer this coverage.
Uninsured / Underinsured motorist coverage - this one becomes a little more complex and is designed to cover you for bodily injury you sustain as a result of the other driver's fault and often only kicks in after their bodily injury coverage is exhausted. Again, this is not a mandatory coverage and your policy may or may not provide for this coverage. If it does you will likely need an attorney to pursue your own insurance carrier for your recovery.
Personal Injury Protection - this one is very much akin to Med Pay, and is a required coverage in states that are considered "No-fault" states. If you live in a no-fault state, your policy will be required to provide this coverage, up to a capped amount that you select and it will pay for your out of pocket medical expenses regardless of who is at fault in the accident.
This is not an exhaustive list of coverages you might have on your policy, but they are the main ones. Other coverages your policy might provide for include towing coverage, safety apparel, loss of use, trip interruption etc... just depends on what you purchase. That's why there is no "Full Coverage" in the true sense of the word.
The following coverages are the ones that we are all usually required by law to carry to cover our own negligence. Meaning that, these coverages are not in place for us to recover from our own policy, but to protect us when we are liable (at fault) for an accident. If you are not at fault for the accident and you submit a claim to the at fault driver's insurance carrier, these are the applicable coverages -
Property Damage - this is coverage that will pay for the damage to your vehicle and other damaged property, IF the other person is deemed to be at fault. There is no applicable deductible. You may or may not agree with their insurance company's valuation of your property and the subsequent offer made by the other person's insurance carrier. In this case, you can turn to your own Collision coverage (explained further below).
Bodily Injury - this coverage applies to any bodily injury you sustain due to the fault of the other driver. The other driver may have the minimal amount of coverage required by law and your injuries, especially if on a motorcycle, could easily exceed the amount of coverage the other driver carries. That's why it is very important to consider purchasing Uninsured / Underinsured Motorist (UM/UIM) coverage through your own carrier. Bodily injury and UM/UIM damages can be very subjective and often require the services of an attorney to sort out the details and ensure your rightful recovery. Remember, these coverages only apply if you are not at fault for the accident!
These are the only two coverages that might apply to you from the other person's policy.
So now, to the question, why would you use your own insurance when the other driver is supposed to have insurance?
It may be that you don't agree with the valuation/offer made by the at fault driver's insurance company for your property damage. Whether you do or don't agree with their valuation, it doesn't hurt to have your own insurance company estimate the damages and make you an offer under your own policy. The only caveat is that your deductible will apply if you choose to accept your carrier's offer. However, your carrier will pursue the at fault driver's carrier for reimbursement of what they paid out to you and in many states are required to pursue your deductible amount as well.
As to out of pocket medical payments for your injuries, you should most definitely submit a claim under your own policy for Med Pay (if you purchased that coverage) and/or Personal Injury Protection (PIP). If you are in a no fault state, you definitely have that coverage on your policy since it's required by law, so you should take advantage of that coverage.
As for reimbursement for bodily injury, the value of your claim can get very subjective and will possibly require assistance from a personal injury attorney. If there is any question as to who was at fault for the accident I suggest that you consult an attorney. Generally speaking, an attorney will only charge you a percentage of the recovery. Far be it from me to support personal injury attorneys, but there is the occasional use for them, beyond just filing empty oceans.
I hope this little recap helps those of you that might have the misfortune of finding yourself having to utilize your insurance coverage or file a claim with the other driver's insurance carrier. It's one of those things in life that it sucks to have to pay for but you damn sure don't want to be without it when you need it.
Safe travels...