"Bro" is short for brother the same way that "gay" means "happy". Well, sure, that's trivially true, but it kind of matters what people actually mean when they use a word.
Of course you're right; I have a biological brother and we don't call each other "bro". Here's what google turns up: http://www.npr.org/blogs/codeswitch/2013/06/21/193881290/jea... ...though I'm sure a bit more searching will find more direct treatments out there of what "bro" means....