I believe you've seen the molex to barrel adapter that takes 5 minutes to make. It's a lot safer power if you have the PSU for it. Yellow 12V line to the inside shielded wire, and the two center grounds on the molex to the outside braided ground.
The two Jally PSUs I've butchered have had a red and black wire inside, no shielding. Red is centre positive. I just solder on to an old molex fan cable (I've heaps of them from years ago), bit of heat-shrink, job jobbed.
True, if you crack the case you will find that. However oddly enough I have a use for old jally supplies, one is powering a beautiful halogen lamp that had it's power supply die years ago (4 amps at 12 volts needs a big power supply). The other is for a peltier cooler based fridge that had it's power supply (12 volt 4 amp) die as well. So oddly enough how can you screw up these things if the jally supply decides to explode :-)
They would also make good 12 volt battery chargers oddly enough.
C