The amount of power that can go through the cable depends on a lot of things. The only thing I can think of that could possibly create enough heat for that to happen is a DPP44 switch power inserter. The most power a dish receiver, that is operating properly, will ever output is 20 Volts @ 750mA. That's only 15 watts of power (DPP44 switch is 28V @ 2000mA, or 56 watts). Beyond 750 mA(and actually as low as 650mA) the power supply will either drop the voltage to keep a continuous amperage, or cut off the power for a few seconds and try again. I suppose if it was localized enough 15W might be able to do that, but I'm wondering if there is either an open ground, or a hot ground on that electrical outlet causing the receiver to place excessive current on the shield of the cable that was grounded out when the flat cable's outer casing was broken, and the sheild came into contact with the metal door.
Just out of curiosity, what type of receiver was plugged into this cable? and did the fire marshall ever test the electrical outlet that the receiver was plugged into? If so did it have a valid ground?
For the argument of FCC vs apartment complex management, the management can legally say that you can't drill a hole, or use unsafe cable, as the FCC rules have exceptions for policies related to safety. If whoever does installs in your area got the UL listed flat cables, instead of the cheap one's they put in, there might not be anything the management could say about it.
My office uses only the TFC Amphenol cables, and we use quite a few of them, and I have not in my 2.5 years working there ever heard anything about fires, or even melted flat cables. I have replaced many of them due to damage, but not a one even smelled like it had melted a little. I have had to replaced flat cables like the one that was installed at the OP's apartment (installed by a contractor months before) with the right ones due to severe damage and none of them had any burn damage either. Makes me wonder what was different in the OP's apartment.
GoalieBob, yes it is a dishnetwork requirement to check the outlets before an installation, but that does not automatically move liability to the tech if the electrical outlets are bad. There is no law that says we have to check the outlets (at least not in my state) it's just generally a good idea. If I put sugar in my gas tank because it's cheaper than gas, then take my car in to get the brakes fixed, is it the brake shop's resposibility when my engine sceizes up 5 miles down the road from the brake shop? Nope, you're gas tank, you're responsibility.
heyjude, keep us up to date, I'd like to know more about the outcome of this.