Yeah, it is a green car (special car) icon on the map, no wonder the moment I picked it up I got rammed senseless from someone random in a blue sports car, the car was up in the mountain and I too some serious risks driving off road with it to get away, flipped and rolled it lots of times, twice landed on the roof and just had enough momentum to turn over. Thought I would die/lose the car about half a dozen time, it was battered as a result. I only lost him when I drove towards a cliff, braked hard, waited for him to ram towards me and moved over just enough so he went down the cliff! I bet he was annoyed with that! Then I limped to Los Santos Customs and the second guy caught me when I as was coming out after a repaint but had no idea where to drop the car off.
As for getting targeted, I try not to get involve with randoms. Most of the time when free roam I just rob a store, buy new clothes, steal random cars to get around and then sell it. The time when I was getting targeted while inside the store was weird. The car wasn't even my personal vehicle, yet he kicked it, and tried to blow it up by pouring petrol on the car/ground and shooting at the fuel in order to blow the car up. Which was pointless as I will just steal another. Oddly, his plan didn't work. Then he lingered and fired rockets at the store front. I just watched him from the window, and taking pictures. He died trying though when he drove through the door of the store and flipping the car.
I swear one time someone invited me to their apartment just to kill me. So I never left his apartment, stayed there and drank whiskey, watched TV, eventually he sold his apartment and I got ejected !