Ted, I also have no dog in this fight. I have never owned a Parker repro, and probably never will... unless one pops up at a give-away price... never say never.
So the only photo we have to verify a Parker repro with a separated barrel lug was taken by you. That seems rather odd, if this is anything close to a common or widespread problem. Especially in a time where virtually every cell phone has a camera. If it was commonly happening, people like the Preacher would be collecting every photo they could find, and hysterically posting them on multiple firearms forums dozens of times. And for all of the panic over small bore Ithaca Flues frame cracking, we still don't see evidence of even a dozen different guns... out of nearly a quarter million made. And it appears the few that actually did crack at the breech/water table juncture... were severely abused.
That's why I refuse to rush to judgement about these Parkers. I went for years believing that small bore Flues frames were prone to cracking in normal use. That turned out to be bullshit, like many things posted on the internet.
There may be 18 other broken Parker repros out there... or there may be many more... with other potential failures on unfired guns. All anyone needs to change my mind is some verifiable proof.
I have already noted that the braze joint in your photo was indeed a bad one. I see roughly 50% wetting between the two mating surfaces. Some of the bare spots are on the barrels, and some are on the lug.
What we cannot know from a photo is the braze material that was used... the temperature of the parts during brazing... the flux used... the fit of the pieces being mated together... the clamping stability and pressure... contamination of the surfaces... the skill of the person who did it... etc. Analysis by a good metallurgist could tell us a lot. We also don't know what happened at the point of failure. For all we know, the barrels got launched from the gun after being fired with nuclear reloads assembled by the Nutty Professor.
The difference between repairing a braze joint vs. a solder joint lies mainly in the materials used... and an increase in temperature for brazing. Brazing happens at greater than 850° F. and solder less than 840°F. Shotgun barrel rib soldering is normally done with alloys that melt around 400-450° F. Brazing is normally stronger than soldering. But both must be done right.