I agree with that. Here's what I think:
Mario and Luigi are brought into the world by Mushroomian parents in The Mushroom Kingdom. Kamek, predicting their futures, tries to kill them before they can grow up, so their parents bring them to Brooklyn and give them to Italian foster parents, the father being a plumber/carpenter man, and they learn handiwork and such, and gain their Italian accents.
They grow up in Brooklyn, Mario dates a girl named Pauline, DK escapes or somehow gets there and captures her, and he makes one of his first conciously heroic acts in saving her. Shortly after, he's contacted by the Mushroom Kingdom in lieu of the fact that Princess Peach Toadstool, their crowned ruler, has been captured by King Bowser Koopa of the Koopas, who wishes dominion over them, and they need Mario and Luigi's help...
*****************************
Mario`s adventure is over for now, but,
Mario`s dream lives forever...
Dream on, Mario... dream on.