Stained truck

Recently, my 2023 Tundra TRD Sport was oversprayed with wood stain while at work. A claim has been filed with the responsible party's insurance company. The adjuster came out, looked at the truck, and assessed the damage. It's on the paint, trim, blackout material around the doors, all the glass, and even the wheels and some spots in the bed.
He confirmed that they would be responsible for fixing it. He asked me to try rubbing lacquer thinner on an inconspicuous place to see what would happen, which I told him I was unwilling to do. He then said that they wanted to try an initial step; if that didn't work and a paint job was necessary, then that would be the final fix.
My question is, has anyone had this happen or have experience with wood stain on car paint? Any suggestions for reputable people or locations near the DFW metroplex in Texas who could get my truck back to its original condition would be greatly appreciated.

 

Should using oem paint materials be a concern for longevity of my paint?

 

Same happen to my wife 2018 grand cherokee. Had detailer clay bar the car. The windshield was more trouble. Razor blade took some time. The clay bar did the trick and even though it was over sprayed it wasn't bad.

 

Paint or stain?

 

Stain.

I had some roadway paint I ran over in my Tundra while on the job one night. I didn't even know I ran over the paint and had splatter the driver side. I went to do a quick wash and noticed that the drive thru car wash didn't do a good job. Then I tried to rub it off and came off kinda easy with my nail.
Then noticed it on mirror and flares. So I went to a detailer retail shop to find some to help remove the paint. Little clay bar did the trick. Not sure if my truck being dirty helped it not stick or good ol ceramic coating.