Perhaps I should have included another sentence in the quote: it startsWhy not? Assuming that the fuse is in the hot line AND the plug isn’t polarized, if the plug is reversed, the fuse is on the neutral line. From plugged in device hot, through the fuse, and to neutral, is a dead short. The device neutral is protected for 15A; the iron is protected for 0.5A. The iron fuse will blow.
" IF your iron has a three wire plug then the tip is grounded. "
So, from my limited knowledge of American plugs, it means that live and neutral must have been correctly connected (although that is irrelevant)
The tip, being connected to earth, was accidentally connected to a circuit that was live. Current flows from the circuit being worked on to earth, through the soldering iron's earth connection. It doesn't go through the soldering iron's live or neutral, so it doesn't blow the soldering iron's fuse.
