Ed: I don't disagree with what you're saying, I just don't think it's relevant to discussions of DNA. We can call Pluto a potato, does not change anything. As to classification the trend is clearly to call them the same species we just need to let the old scientists die off ;)
So, in theory you can have genetically compatible separate species as soon as they are no longer capable of interbreeding. However, as Humans and Brown bares are both biologically capable of interbreeding and live in such a manner that the do interbreed they don't fit that definition. Temporary barriers are not necessarily enough as they may exchange DNA in the future.
PS: Ring species are considered a single species because a mutation can start at one end and given time make it's way around the ring. Thus they are a single pool that can and will exchange DNA.
No, that was one long discredited idea of species. It has not been used in decades. Why are you so insistent on pushing this false claim that brown bears and polar bears are the same species? Look it up, they are not. One is Ursus arctos and the other is Ursus maritimus. There is no ambiguity or dispute.