Urban legends, I'd think. The further the bullet has to travel the more impact environmental conditions will have on it. (wind, etc.) I'm sure things as mundane as the humidity level in the air will impact it as well. I doubt even an excellent marksman could hit a human-sized target 1 time in 100 tries at 2.5 miles, certainly not with a 7.62 round. Barrett 50, chances might rise a tiny bit (heavier bullet, less deflection from wind, etc.) Also, at shots at that kind of range, you need to account for the curvature of the earth as well as the impact the earth's rotation has on the shot, which will differ depending on what latitude you're at. Not to mention, the velocity loss at that range means the round isn't going to do much when it gets there, unless it itself is explosive.
So, ultimately, while it might be POSSIBLE to do, the odds of someone being able to do it even remotely reliably are about nil. OK, just did a quick Google. Here's something from the UK's army's own website:
Sniper Rifles
The L96 Sniper Rifle is accurate enough to achieve a first round hit at 600 m and achieve harassing fire out to 1000 m. The rifle is normally fitted with the Schmidt and Bender 6 x 42 telescopic sight. The front bipod is fully adjustable and folds away when not in use. Eight trained snipers are equipped with this weapon as part of Manoeuvre Support elements within the BG. Snipers are masters of camouflage, concealment and operating alone for long periods. L96 fires ball and armour-piercing ammunition.
The L115A1 8.59 mm Long Range Rifle (LRR) provides units with enhanced sniper and sharpshooter capabilities. LRR fires ball and armour-piercing ammunition.
L96 Sniper Rifle
Calibre: 7.62mm
Weight: 6.5kg
Length: (adjustable) 1124-1194mm
Muzzle velocity: 838m/s
Feed: 10-round box
Effective range: 900m, harassing fire 1100m
L115A1 Long Range Rifle (LRR)
Calibre: 8.59mm
Weight: 6.8kg
Length: 1300mm
Muzzle velocity: 936m/s
Feed: 5-round box
Effective range: 1100m plus
Now, 1100m is about 3600 feet, or just about 2/3 of a mile. Now, it says 1100+, so fair to say it goes out to 3/4 a mile, or maybe even a full mile.
Now, as for the Barrett 50, here's what
http://www.snipercentral.com/m82.htm has to say:
Max Effective Range 1830 meters
(Note that in the article where someone tested it, they found the real ranges to be more 1000-1500 meters, but we'll go with the manufacturer's claim). 1830 Meters is about 6000 feet, or a mile and 1/8 or so. So, given that even the Barrett manufacture doesn't even claim an effective range of even half of your lower estimate, I think it's pretty safe to claim snipers aren't going to be taking people out at 2.5-3 mile ranges with rifles. Hell, even the .50 cal heavy machine gun (which is too heavy to really be terribly man-portable) only lists an effective range of 2000m, which is about 1.25 miles.
About the only infantry carried weapon that will reliably reach out and at least get close to someone who's 3 miles away is a mortar. So, I suppose if you wanted to assassinate someone 3 miles away, you get a laser homing mortar round, get someone to paint the target with a targeting laser, and lob a shell on over.
-Arlos