Not sure of his temperatures but are you saying fermentation temps at 12 psi will carbonate fully? I have a hard time believing that. The 28 psi mentioned above is more in line with what I've seen, which is obviously impossible in the fermenter.
Here's my understanding of the process, and why I said what I did (subject to adjustment by anyone with better understanding than mine). His beer is carbonated although probably not all the way.
One of the Low Oxygen processes is spunding in the keg. This means transferring the fermenting beer to the keg when it has about 5 points of gravity to go. For instance, if final gravity will be 1.012, transferring when gravity is 1.017. And yes, nailing that is problematic, but that's the approach.
Beer fermenting 5 points of gravity will produce about 2.5 volumes of CO2. If you look at a carbonation table, you'll find that's pretty much in the middle of where we want to be.
So--as the yeast finish fermenting that last 5 points of sugar, the CO2, since it's not being vented, has to go somewhere. It goes into the beer.
This is not unlike what happens when you add priming sugar to bottles for conditioning and carbonation. That carbonation gets absorbed into the beer. What's more, the yeast act as if they were billions of tiny carb stones, meaning the CO2 is absorbed right into the beer.
In essence, then, we're "bottle conditioning" in the keg when we do this.
So--I'd expect CCHart's beer to be carbonated. It likely isn't as high as he might want but if not, it'll be somewhat carbonated. What he'll need to do is chill it so the headspace CO2 is readily reabsorbed into the beer, and then see what he's got. I'll bet he's in the ballpark but not there.
***************
I'm still working all this out, including exactly how to account for the amount of CO2. In the keg, there is little headspace, so the CO2 has to mostly be in the beer. However, I have a Spike 10-gallon conical fermenter. I brewed a 5-gallon batch on Thursday and put it in the fermenter. While that was transferred to the keg with about 5 points remaining, I discovered an issue I need to resolve.
And that's this: while there isn't much headspace in a keg, there is in the 10-gallon spike conical fermenter when I only do a 5-gallon batch. If I were to pressure ferment in there as CCHart did, I won't get the full 2.5 volumes of CO2.
The reason is what you noted above. The system vents at 15psi. The CO2 produced is partially forced into the beer, but much is vented. To get beer carbed to the level we'd want, you're right, at that warm temperature he'd need to spund at 30psi more or less. He can't so the beer will be partially carbonated.
But when we spund in the keg, there is no venting so it's essentially the same as bottle conditioning.
I hope that was clear. It's an interesting process and one that we can use if we understand it correctly.