Pipes come in contact with the Earth at some point, so this gives them the potential of the Earth Ground. Furthermore, "Back In The Old Days" the plumbing was grounded to a grounding rod, often the Fuse Box was also attached to this grounding rod in the basement, and so was our Water Meter's Ground.
This means, if you attached one probe to the hot of any wire in the home, and the other side to any pipe. Then it is the same as attaching the second lead to the ground itself. Which means, current will pass from the hot through the meter to the piping to the grounding rod and to the Earth Ground. This is why you will get a reading, this was the normal procedure for grounding in those days.
conduit was also attached to the grounding system so you attached your ground wire from the junction box to the conduit to ground the box as well.
Run your ground from the outlet to the back of the box and it too is grounded.
Cloth insulation was used prior to 1968 I would guess, but by the 70's it was not used any longer. In fact, when we remolded my parents home back around '76 the cloth insulation wiring was considered old then - so now I think the cloth covered wire was probably stopped in the later '50s.
This is not a type of wire you want to continue to use in today's world. That wire was aluminum and not copper. That means, it has a much lower melt point because it will heat up a lot sooner than copper wire. It wll not carry as much current as copper, in other words, and if you do try to draw that much current on this line it will heat up very rapidly.
So what i think happened here is when the insulation came off the wires shorted out when they touched and this caused an immediate flood of current to pass from one line to the other - there was next to no resistance in the path to prevent the flood of current.
In turn - the aluminum wiring heated up very rapidly and this happened so fast the breaker did not even have time to respond until it was too late and the wire caused the breaker to be destroyed. The wire itself could be totally ruined at this point. The only way to 'Fry' the breaker is with extreme heat from the wire.
Normally, the breaker will detect the excessive heat and have time to kick - off, but again if it heated up so fast the breaker did not have time to respond. I could have just passed the excessive heat to the breaker's contacts and melted the plastic housing - which is what i think you mean by 'fried.'
This heat problem with aluminum is also the number one cause of the insulation becoming brittle to the touch, and if it happened at your point of contact it has happened along the whole stretch of the wire as well, if anything ever came in contact with it in the past few decades.
Leaving that wire in there and using it is a great potential for a fire. Like most things in electricity, if the potential is there for it to happen, then given enough time and it will happen.