Okay, I did a quick input delay experiment. I didn't do this very thoroughly so this could be off by one or two frames.
SC4 PS3 didn't have better offline input lag than SC6 on PS4. It seems to pretty similar, with it possibly being 1-2 frames worse. I got similar results in SC5 but with much higher variance in input delay, with the best being same as SC4 and with the worst being 2 frames slower.
Playing against the same opponent in SC4 and SC5 (with the game showing a 5-bar connection. I'm not sure what ping I get to the friend, but it should be somewhere between 30ms and 60ms), I had 5 frames (aka 83ms) more input lag in SC4 than SC5. I couldn't compare to SC6 as the game somehow refused to establish a good connection between us. I dunno why (normally SC6 works fine for us).
With the ping to my friend being pretty darn good, it makes no sense that SC4 fiddled around for an extra 83ms before showing an in-game re.