There have been several confirmed sniper kills over 2,000 yards in modern times. Also, one in 1967 to Carlos Hathcock. I have no idea if these guys could "target shoot" at these distances, but they managed to get confirmed kills. There are people out there able to reach a mile as well. Which is a little over 1700 yards I believe. A quick youtube search shows some videos at 2,000 and even some over 3,500 yards but I didn't watch any of those. Some of the more knowledgeable guys will have to say how far they've grouped on paper.
-Jake