It will (I think) always reflect a rebuilt title. A car that is in an accident is often "totaled" if the repair cost exceeds the blue book value.
For example, I had a 95 Chevy S10, my daughter crashed it and the repair costs were $4,000 (estimated) more than the blue book. The insurance company paid me for the value of the truck and THEN I bought it back. I fixed it and drove it for years before I junked it. The title was always a rebuild title but who cares, it ran great and I kept it until the truck was beyond economic repair.
In your case it seems there are conflicting stories but if the insurance company paid it off and then it was recovered the only way to retitle the car is to issue a rebuilt title; in my case there was damage but was easy to fix.
I recommend buyer beware and think about your future with the car; for me I keep them until they cannot be repaired/fixed/maintained economically.