Why? I thought he just saved it by redirecting Big Mam's wrath from the island to himself.
But yeah, Luffy nonchalantly answering the phone instead of the hesitating Big Man's underlings was a jolly good and very Luffy-like thing to do. Things like that unequivocally mark him as a man of huge calibre personality wise. You can be as powerful as you want, but if you hesitate or think of consequences even for a moment, you can't walk alongside the big players.