Working from memory, but I always thought that a Mob War automatically started when there were 6 or more characters on the wall, it had nothing to do with characters on table(i.e., in hand). The start of the Mob war was automatic, and continued until there were no character cards left on the wall, once character being eliminated (buried) at the start of each players turn.
Maybe when in the end, there are less than 6 total characters left in game (either on wall or in hand), then the Mob War is automatic and a given?
There is exactly such a rule as you discribe last. And which is also what was replied earlier - there is no talk about the general rule for starting a mob war (which is just as you discribe first).