I have played this game for years. But every time the legion knows. How, long range shots, silenced weapon, no survivors. How do they know ? My stats make no difference.

have you tried being hidden while you do kill something?

Is your weapon silenced? Make sure you have the right weight requirement to use the weapon. Make sure you're hidden before start fighting and only go for headshots. I find being a sniper tricky at first but it's easy after some time. Also if regular guns are giving you a problem use energy weapons. They require less strength and I find them just as good for being a sniper. All you'll need is a laser rifle and a scope until you get the YCS/186.

Have a silenced weapon, make sure you sneak and your status is [HIDDEN], and make sure you can kill them in one shot.

Then wait until your status turns to hidden again before picking off the next one. You might need to move around a bit before it'll return to hidden. If your status turns to flashing [DANGER], that means you've been spotted.

.308 JSP or AP. Make sure you are CROUCHING and that it says (HIDDEN) at the top of the screen. Use a SILENCED sniper rifle.

Unless the question is: "How come when I stealthly take out the Legionaires, I keep getting Vilified by them?" Then that is just game Mechanics.