One point he fails to mention is that when a significant amount of the highly volatile fractions have evaporated the petrol becomes harder to ignite, it has 'gone off'. This is not likely to become significant with large quantities stored in sealed cans over a reasonable length of time. But with smaller amounts stored relatively open, ie a carb, then the more volatile fractions will evaporate first, and quite quickly. What's left becomes harder to ingite with time as more and more of the higher fractions evaporate. The effect is most noticable on fussy starters. With my XT225 if I just switch the ignition it off, turn off the fuel tap and leave it for a couple of weeks it can be a bugger to start on the fuel that's been sat in the float chamber. If I turn off the fuel tap about 1/3 mile from home so I get back with an empty float chamber. Then when it comes to start it I open the tap and fill the float chamber with fuel from the tank and it starts fine, even if left for months. So yes the fuel does go off, but not as quick in the tank as it does in the carb.
Regarding OF's lawnmover, we have similar experince with our petrol pressure washer which is just used during the race season, that needs fresh fuel after being left for usually about 4-6 months. It is a fussy starter and it has a small cheap plastic tank with screw cap that doesn't fully seal, if it's not upright you do get visable sepage, so it's no suprise that the volatiles do escape.