That might be true, but let's be realistic, the material seems like plastic and if you look at the analogue board pictures above, you can see the other corners look alike, but the bottom left corner is out of shape, this leads me to believe that it was made to handle certain amount of heat and on that one corner, the amount of heat exceeded the operating temperature and it just melted. So something happened that should not happen normally.
If your meter will read really low resistances you can measure the shorted rail in different area's or the board and the reading should get lower the closer to the shorted component you get. I haven't ever done this personally but have seen it done online a few times and it seems to work
Other than that what you have described should work in most circumstances (It's what I would usually do on modern boards) however it will not work on really really low resistance shorts (e.g solder bridges)