Okay, birds does not mean stool pigeons per se.
It's a mafia term -- but specific to the North American mafia (Ndrangheta, Cosa Nostra, etc... out of NYC, Montreal, Hamilton --yes, the Hammer is a mafia hub -- and Toronto.
It's a generic insult. Once upon a time it may have come from a derivation of stool pigeon, but now it's just an insult commonly used without a specific intent anymore i.e., "That guy is a fuckin' bird".
It's almost like "goof" in prison -- it has an original etymology, but now it's just the holy-of-holies of insults.
You guys will have to take my word for it. Many years of working in rehab, and also being Italian, I'm familiar with it and when he said it -- it was like a thunderbolt. Clearly a guy who is or is in frequent contact with gansters (which we already knew). And if you can't take my word for it, I'LL GOUGE OUT YOUR EYES AND RIP OUT YOUR THROAT IN MY UNDYWEARS BLAAAAARGH!