If you're like most everyone on the planet you hold your controller like this.

Which is fine, until you get to a point where you need to press one or both of the buttons quickly and repeatedly. Like in the Wii Punch-Out!! game, where you have to rapidly press the 1 and 2 buttons to regain health. And unless you have some kind of SuperThumb(tm) you're just not going to be able to press those buttons as quickly as you'd like, at least not for very long.

That's why, when the situation arises, I quickly flip my grip around so that my index and middle fingers are on the button (or buttons) that I need

That way I can tap my fingers back and forth to press the buttons far faster than I can with just my thumb

With the added benefit that my thumb doesn't start to cramp after a few minutes of button-mashing, which is always a plus.