I have spent a ton of time trying to find the answer to whether they can determine if the stain came from dead body, it appears that the answer is they can get DNA but they can't say it came from a body. The only cases I could find were three like you mention, they found so much blood the person couldn't be alive. It doesn't sound like this stain is that big.
The other cases I found that didn't have a body had other incriminating evidence, like witnesses etc...
The air test that they were talking about this morning is newer technology and hasn't been used/challenged in court yet. Hopefully the evidence they haven't shared is really good, or my research skills suck and you can determine if a stain came from a body.