It's mostly a throw-away line, one of those explanations that doesn't explain much and yet purports to explain current circumstances in a way that allows for a new topic of discussion ... a way to dismiss some unlikely thing that just happened:
When pigs fly ... anything's possible.
But, for just a small moment, what if it were true? What if "anything's possible" meant precisely that?
What would that do to all the interior and exterior dialogues in which one thing or another were designated as "impossible?" If all things are possible, then calling any of them impossible would really be screwing the pooch, wouldn't it? If even the smallest thing were "impossible," then the whole "anything's possible" house of cards would tumble.
Anything's possible, I guess.
Or impossible, if it suits you better.