I think it is clear that James Naismith's original idea spawned both basketball and netball.
if you follow that argument then association and rugby football were both invented by the same people, or by inventors unknown, as both are spawned from the same pre-existing game.
to me the origins of most games are lost in time -- it's easy to imagine that people kicked, threw, bounced and batted balls of all descriptions, and ideed threw them through hoops, for 100s of years before anyone had imagined formal sports.
a sport is different from the folk-games from which they all spawned : a sport is no more than its laws/rule and a sport is invented when its laws are codified