Right, but if you compare the number of times in a given season there's an empty net, versus the number of times goalies have scored you have to come to the conclusion that luck was involved in each one, if not it would happen more often. Are some stranger than others? Sure. But every time a goalie scores it's strange, so again...splitting hairs.
Edit: Actually, according to this the majority of goalie tallies have come in the same manner as Brodeur's last night. As such, statistically it's far "luckier" to shoot the puck and score for a goalie than to score as the last person who touched the puck before the opposition shot into their own net.
That makes no sense. You are misusing the word lucky. It's lucky to have the other team throw the puck into their own net versus you actually taking the shot at an empty net. The reason more goalies are credited with goals that go in like this one last night is because most goalies don't try and take that shot. You mean to say it's less probable for a goalie to score by shooting the puck versus touching it last and having the other team put it in their own net. Not "statistically lucky" which is basically an oxymoron.