FAIL.
Grip does not tighten the crosshairs on any gun, there is one exception though.
The SAW with Grip + Steady Aim has tighter crosshairs, taken from
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"-M249 SAW with a Grip has improved Hip Accuracy (Between Assault and SMG hip accuracies)" - Now, if you do this glitch correctly on the SAW you will have tight crosshairs and a RDS.
The character doesn't hold the Grip with this glitch, but the grip is still attached.
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I'd like to say though, I'm still not 100% that this glitch does actually work, the fact that the SAW is like this though makes me wonder...so don't have a go at me if I'm wrong.