I love sniping people, but I really don't like using the AMR for it. I find the magnification on the scope to be way too small for my personal preference. I'll admit that it does have incredibly low spread.
the idea in mind is "one shot, one kill" - a missed shot causes the group of Legions to start wandering around aimlessly, looking for the shooter, it makes it difficult to snipe them when they're moving around like malfunctioned robots lol.
ive tried using the sniper rifle with all the mods (high skill also) but on some characters two shots is a kill because of their armor.
additionally, ive given Raul the sniper rifle, he seems pretty darn good at sniping himself, appears to "mimic" what im doing, but i generally let him use the rifle in certain situations since his revolver at this point terminates death claws with 3 shots
ive got to wonder if your companions "learn" your habits, if this is an intended feature in the game.
another suggestion if youre sniping from a distance like me, dont take the "bloody mess" perk, you will find it extremely difficult to find the gibs (body parts) to loot the wares.