Link one - IMO the outlet was bad or the connection to the house cabling was loose. The poor connection led to increased resistance and heat causing the outlet to burn. This was also addressed by one of the posters below the OP. It had nothing to do with the surge protector on the output side of the UPS, I call BS.
Link two - The document makes perfect sense. Nowhere in the document does APC warn against fire. That's because there won't be any. On the input side they are concerned with yahoos overloading the surge protector/power strip and that the UPS would see a low voltage condition and trip to "back up" and back again frequently. They are overstating the obvious, and apparently they have to. Everyone should know the rating of the outlet(s) on the circuit, and avoid running the circuit at close to it's maximum. If you want to draw a lot of power then verify which outlets are on the same circuit and different circuits and split the load up. Pretty much just basic common sense aye?
As for putting the surge protector after the UPS the same applies. Everyone thinks they can buy a 500VA UPS and then just load the he!! out of it and it will handle the load with no problem. Again, use a little common sense and don't exceed the rating of the UPS, preferably leave a little head room as well. The only problem that they indicated was with a surge protector that additionally employed EMI/RFI filtering. Their concern in that case was that apparently this caused distribution problems in the surge strip so that some loads would not receive an adequate current. So they say use a power distribution unit. I assume they are talking about a standard power strip, but I can't be sure. If you use a surge protector without EMI/RFI filtering it would be the same. As I stated in my post above the only difference is the MOVs tied to ground, and they don't conduct unless there is a surge. I use one after the UPS, but not for protection just because it was handy and I needed additional outlets. Also plug the computer into the UPS directly and the peripherals e.g.,speakers, routers, modems etc. into the power strip, because they draw less current and are less sensitive.