I have several licensed suppressors for my powder burners and can attest to the fact that it does help accuracy. For me, I think it's probably from reducing the recoil.My state has just this year allowed air rifles for big game hunting.I hate to start cutting down the barrel and losing feet per second because that equates to loss of energy on the target.Not to mention the game being able to see that slow-moving slug coming at of them and jumping out of the way!
There was some experimentation in UK using 12 fpe .30 for ratting. A conclusion was that at around 300 fps mark rats were able to dodge the bullet. At 500 fps (.25 at 12 fpe) they had not enough time to react.
I think the rat is reacting to the sound...