There's nothing wrong with knob and tube wiring. In fact, some aspects of it are safer (other than it doesn't have a ground wire.) The insulated wire is not in contact with the wood - it's run through insulators, even where it passes through the wood.
And, that old knob and tube wiring wasn't the reason for your problem.
No one's pointed out that those are 30 amp fuses. The wires going to that fuse box are NOT rated for 30 amps. That was a fire waiting to happen. But, you got fortunate. And, that didn't cause the fire either.
In the aftermath it turns out the guy upstairs who 'fixed' the fuse just pulled it out and rammed it back in like 8 or 9 times as hard as he could, and then left it.
Sounds to me more like THAT is the cause of the problem. Apparently the fuse failed like it was supposed to (or failed for some other reason),
but rather than replace the larger fuses inside that part that pulls out, someone decided to "make" them work.
edit: Also, if I had to date the wires going into that fuse box, I'd put them around 1975-1980ish, at least the wire on the left side. I've worked with that brand with that style of covering before when I was a kid. I've never heard of the Dutrax brand of wire though, but the plastic coating makes me believe that it's newer than 1970.
As far as the amount of current going through there - sure, there was probably a lot of current. But not as much as some people might think.
