I thought Tessa was telling Dean that "angry spirits" were born from those ghosts that refused to cross over, not that they turned into demons.
Yeah like I said, I was speculating. What you have is all the text supports. But it was also obvious from other episodes that ghosts can have very different personalities than when alive. Remember the episode with two ghostly victims of the accident. The lady who had been driving the car did not even know she was dead, but also seemed to have a lot of what she was when we she was alive. The guy who had been crossing the road and was hit knew damn well he was dead, and kept torturing every anniversary of his death. And the torturer, who had been a nice guy in life, was not really even seeking revenge any more. He had figured out that torturing her spirit was what let him stick around, and he did not want to move on. And he seemed to have a lot less of his original self left. He also seemed to be very powerful compared to her - able to burst through windows and move things around. You could extrapolate from that to angry spirits losing more and more of their old personalty, turning more and more to evil, growing more and more powerful, and eventually becoming demons. Some people speculate that many of the gods in old polytheistic religions started out as spirits in ghost stories, and that as popular spirit characters attracted more and better tales, they started being described as gods instead of ghosts.
And this kind of speculations is not really an attempt to read the mind of writers, more an attempt to fill in a gap. Since, as someone put it upthread, the theology in Supernatural was scribbled on a napkin in the men's restroom, for some of us it is fun to figure out a more consistent world based on the hints dropped - even if we doubt the writers have thought it through that much.
So the point of the speculation is that it would make a good background for the series and is not absolutely contradicted by the series (so long as we assume a great many unreliable narrators). I suspect the series writers are actually going for a more conventional heaven/hell scenario.