They target you, the car just happens to be in the way of your funeral. Helicopters are the worst, the guys in the ground cars aren't too much of a problem if you're importing/exporting a Super-class car, but if it's the Roosevelt or the Z-Type, any muscle car aside from the Sabre Turbo Custom (or even my beloved Stirling GT) you're going to incur lots of repair costs.
That being said, the lower the market value of the car in question (the actual price, not what you get for selling it) also seems to affect how difficult the mission to steal the car is. Experimented with the FMJ/Reaper/Osiris/811 and I think there's a lower difficulty on the 811 compared to the others (because of the market value.)
I know the game says it scales difficulty based on market value, but whether that's based on sale price or actual price it doesn't say. All I know is that I've seen much easier missions when stealing the 811 compared to any other "Top Range" car, so if you're using that exploit mentioned before, see if your results are similar to mine.