Ha ha! I've seen those little beasts with flaming teeth! What I was thinking was something gnawed on the line just enough to break the insulation and cause a short - then the current would have taken over and melted the line. (still pretty far fetched idea) I was thinking another possibility is a lightning strike - where the lightning chose that point to exit the line and jump to something nearby that was grounded. Seems like you would be able to find burns on something else close by if that were the case.
When I say siamese cable - that is generally a standard coax cable (RG-59 or RG-6) with an 18/2 conducter attached to the outside of it. They are not molded inside the same insulation, but just attached - that way you can pull them apart at each end to get to the two different end points of power and video. At the DVR end you would split them apart several feet - run the 18/2 to the power source and the coax to the DVR.
As for testing - the only sure test is to disconnect the cables from camera and DVR - (have them connected to nothing)- then run a continuity test - there should be no connection between any of the 4 leads (coax center line / coax ground / 12V + / 12V -)
Now - I have assumed that you are running coax or siamese cable because you mentioned BNC connectors - but you mentioned the wiring earlier and it gave me the impression you may be using Cat-5 with baluns at each end. (Cat-5 is network cable with 8 wires inside it twisted into 4 pairs) That kind of wire could be burned through a LOT easier than siamese. Wires are thinner and there is a lot more possibilty of something shorting due to defective insulation.
And then the power supply - yes it has screw terminals for power output. (+ and - for each camera) That is where you would just pull a siamese cable apart - the 18/2 would run directly to the power supply - no ends needed - just screw them down, and the coax goes to the DVR and attaches with BNC connector.
At any rate - having a line burn like that is not just uncommon, it is a little odd! I would think the possibility of that happening again are fairly astronomical.