The pipe they imerge from is in an open area. Over head, a stork has just delivered a Mushroom baby and is on it's way back to the top secret location of the Mushroom Kingdom Baby Delivery Service, when it hears the confused cries of two strange babies.
It takes them back to the storks. The storks only know one thing to do with babies: deliver them! So they pick two parents-to-be in the MK to deliver the new babies to. Off goes the stork.
<insert "Yoshi's Island" storyline here>
After the events of YI, Mario and Luigi are successfully delivered and the stork returns to tell its tale. (Here's where the storks decided to punish Bowser years later by making him raise seven bratty kids.) But the Mushroom people are confused by these twins, and decide to take them to the Chancellor. On the way, they take a break, right next to the pipe Mario and Luigi entered in! Luigi, recognizing the pipe (he's a smart kid) gets Mario to crawl back in with him and go back to Brooklyn, where their guardians in the orphanage have been worried sick about them. The Mushroom parents don't know where they went, and eventually give up looking for them.
So, the Marios grow up in Brooklyn, NY, not remembering anything from "Yoshi's Island." Years later, by fate or just coincidence, they are sucked down that same drain/warp pipe and become heroes of the Mushroom Kingdom.
IF you beleive humans can be born in the MK, you could start at the events of Yoshi's Island and instead of their crawling back in the pipe, their Mushroom parents send them to our world to be safe from Bowser.
There you have it! It's a stretch, I know, but the first thing I thought when I played YI for the first time was, "Okay, how can I keep BOTH storylines?" This is what I came up with.
Hope you like it. Give me your comments or theories of your own.
And, if you liked this, I'll share my "Where do Peach and Daisy come from?" theory.
One more thing: this is just my imagination working overtime, and not officailly Nintendo, nor what anybody has to think. It's just for fun.
Enjoy!