Not sure I fully understand your fact pattern but let me give it a shot. Insurers generally will parse out property damage and bodily injury, but they will not pay your medical bills as those bills are incurred. Basically what they will offer by way of settlement is to compensate you for those bills plus your general damages (i.e., pain and suffering). So I don't think it was any trick by which the adjuster indicated you would be paid directly, but rather a policy of resolving an entire claim at once.
Second, there is no benefit to making a reasonable demand to an insurer. The adjuster looks at that as your starting point and the adjusters are well trained in the fine art of negotiations. What you want to do is to ensure that your treatment is complete before you start negotiating, or make sure that you have received the proper consultations so you can take into account any future treatment. If there will be future treatment then correspondence from an M.D. to that effect will help your case. Similarly, if you are making a lost earnings claim for work missed a result of the accident, having a doctor's letter indicating that you are restricted from working and pay stubs to verify the lost time is mandatory if you want to be compensated.
If this is a small soft tissue claim with little by way of medical bills then the $500 or $1,000 that the insurer is offering may not be a lowball amount at all. However, without knowing more about your claim and the underlying facts, I cannot make any assessment as to the total value of the claim. If the negotiations have broken down, and you are trying to pursue this on your own behalf, then your best bet may be to file a small claims action against the other driver. Small claims or hiring an attorney are the two pieces of leverage that you have if you are not getting the desired result directly from the insurer.
Yes, you should have your medical bills paid by your health insurance as soon as possible to avoid any collection efforts and the like. Caution: some health insurance companies have strict time guidelines to present medical bills. Another reason to get them in as soon as possible. Also, double check to see if you have "medical pay benefits" under your own automobile insurance policy. If you do, you could use this benefit as well. Keep in mind some "medical pay benefits" plan have time frames as well. You will have to reimburse your health plan at time of settlement provided your health plan has a reimbursement provision. You will need to ask for this provision. If you use an attorney, an attorney can many times get a larger reduction on the reimbursement to your health insurance company which helps usurp the cost of using an attorney; it can also help to increase your net recovery at time of settlement. I hope this helps!
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