Well yes, but most automatic weighting tools allow you to set how many bones per vertex. And regardless, a good rigger will adjust the weighting setup by the automatic tool.
I usually shoot for 3 bones per vertex (and not for every joint; most joints will only be 2, but complex joints like shoulders get 3.) Remember: the more bones per vertex, the bigger processing hit. And since for most joints there's only a subtle visual difference between 2 bones per vertex and any more, using more is a waste of processing power. As for 'fan bones,' I'm assuming that's some sort of rigging trick used for cinematic animation that is not a good approach to rigging a character for in-game use.
I usually shoot for 3 bones per vertex (and not for every joint; most joints will only be 2, but complex joints like shoulders get 3.) Remember: the more bones per vertex, the bigger processing hit. And since for most joints there's only a subtle visual difference between 2 bones per vertex and any more, using more is a waste of processing power. As for 'fan bones,' I'm assuming that's some sort of rigging trick used for cinematic animation that is not a good approach to rigging a character for in-game use.