Well I think the whole mention of Stanley Cups is stupid, regardless. I mean, Joe Nieuwendyk only got into the HoF because he won 3 Cups. It should be about the player, not the teams he played on.
I mean, if your argument for Osgood is "3 Cups", I don't know how you can't allow Kris Draper into the Hall of Fame, because he has four. No one would ever dream of letting a thoroughly average forward or defenceman into the Hall of Fame, but it's permissible for a goalie.
By my calculations, Osgood has let in 9 more goals over his career than the average goalie would've (varies season-to-season; most of his years in the 90s he was slightly above average save percentage wise, but he had some truly abominable years towards the end of his career).
93-94: 0
94-95: +8
95-96: +15
96-97: +6
97-98: +11
98-99: +3
99-00: +4
00-01: 0
01-02: +3
02-03: -19
03-04: -1
05-06: -3
06-07: +1
07-08: +5
08-09: -26
09-10: -13
10-11: -3
Can you imagine a forward getting in who scored 9 less points than the average forward over his career? It wouldn't happen. It wouldn't even be debated. Osgood was not even an average goaltender (let alone an average starter) over his career, while playing for some of the best defensive teams in the league. Anyone who thinks he deserves to get into the Hall of Fame has absolutely no clue about hockey, let alone separating individual performance from team performance.