A modded controller can't increase fire rate with rapid fire. The rate of fire is set by game code.
It's likely a glitch, something like swithing weapons, reload glitch, executed very quickly, with specific timing. If that's the case, a controller macro (user defined sequence of button presses) could make it easier to execute.
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That's what I'm saying. The controllers shoots, reloads, sprints, shoots, reloads, sprints so fast with just the shoot button, so every burst from the hawksaw is the first burst in the chain of rate of fire. So yeah it uses a glitch within the game to reset the rate of fire very rapidly. This is just what I have heard they do. Could be false but sounds legit to me.