ok...
for all you skeptics, i pulled out my 2002 edition of NHL's History of the Stanley Cup... lucky for me, it has each game's stats.
the hard part was sorting through all of the games through 75 years of stanley cup hockey in the nhl and writing down the shots of each and every team that made the finals.
the easy part was that only a few series ended with the losing team outshooting the winners:
NJ won the cup over Dallas in 2000, but average shots for NJ per game was 27.4 and Dallas averaged 34 shots per game.
in 1989, when the Flames won over Montreal, they were outshot on per game average 30 to 32.
1984 the Oilers won over NYI, yet was outshot on average 38.1 to 35.2
1983 the NYI won over Oilers, yet was outshot on average 34.7 to 34.2
so far, i have looked back as far as 1974. haven't got to where the leafs have won anything, yet!
i looked at 30 years of stanley cup history and only 4 times did the winning team get outshot on average. but, mind you, this is only the stanley cup finals... chances are NJ, Calgary, Edmonton and New York, probably outshot there earlier playoff oponents in their respective winning years....
also, the shot differencials are very narrow. i still don't think that you will find a comparable to that awesome leaf stat of getting outshot on average 34 to 25.(one to be proud of surely)
also, i still stand to say that you won't win Lord Stanley getting outshot consistently.