If my spouse and I were involved in an auto accident and the at-fault driver's insurer has offered us "inconvenience money", what do we do?

Question Details: It was not our fault. The driver who rear-ended us was insured. The insurance company has assumed full responsibility and is handling the claim. Our auto is most likely totaled. We were both taken to the hospital. I was discharged that night after examinations and X-rays for whiplash. My spouse was kept for observation for 1 1/2 days. The insurer called us and offered $3000 for what they called "inconvenience money" for the trip to the emergency room, tests, etc. They clearly said it has nothing to do with medical bills. It this legit? Are they worried about us suing? We are very cautious. Could you explain what is going on?

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