I was just noting the potential conflict between a para 2 and para 3 in your green warbler example. The two varieties are the same species.
I realize what you're saying and it's an interesting question that I don't know the answer to (i.e., if, for whatever reason, they exchanged gametes would offspring result?) but all other sources I've seen on the Green Warbler aside from the S.F. Chronicle graphic say they cannot interbreed. This may only be due to them not recognizing the mating calls, but there are other clearly different species that "can" in theory interbreed but never will in practice.
In some ways, and I think you already know this, "species" is an arbitrary, problematic concept - designed to assist in our classification of the natural world. The boundaries are frequently fuzzy as one would expect in a backdrop of common descent.