The Poop Talk: Infant Gut Health: Common vs Normal

"It's normal for breastfed babies not to poop for days because breastmilk is all used up". 

This is one of the most commonly shared and staunchly-held myths that comes from as widely disparate sources as pediatricians, nurses, La Leche League, WIC, breastfeeding professionals...almost anyone whose role is to educate parents about infant health....and of course, from other parents and self-proclaimed experts all over social media.

Is this true? 

What's behind this assertion? 

What does the science reveal?