Uh thats intended feature, machine gun has auto-fire anyway
You're technically correct, but I'll chalk this up to not having played Cave Story in far too long, I forgot the mechanics of it.
What the Buffalo Famicom Clone controller's timing interval does, is make sure that your ammo doesn't run down while you 'fly.' Normally, when Quote uses the Machine Gun to propel himself upward, you can only do it for a fixed interval, until the ammo reaches 0, and then you have to sink to the ground while it recharges to 100. But with the particular turbo button interval that the Buffalo Fami Clone has, the ammo seems to "stick" at a certain set of two numbers, alternating rapidly, and only decreasing to the next set of two numbers after a few seconds of time, during which Quote is in the air.
So, yes, the Machine Gun lets you fly in Cave Story, but with this particular controller, it's much more efficient. It's almost like a cheat, but it depends entirely on the turbo interval of the controller.