Arrogance Amongst Sports Fans?

Recently, on Facebook, I have seen a lot of interactions that follow these sorts of lines between a person and their Blues fan mate:

Friend 1: "Congratulations on the Blues win at Wembley"
Friend 2: "Thanks. I think we played a good game and we deserved the win"

As someone who doesn't have any real interest in following team sports, I cannot quite see how fans enter into the intrinsic arrogance of this interaction.
Sure, I know that team sports such as football carry certain promoted ideals of solidarity and unity etc and that fan support means a lot, but surely the language of this interaction carries with it the fan implicitly taking credit for the accomplishment of 11 or so total strangers.
The nearest applicable thing I can think of to relate it to me involves Jackie Chan. Now, pretty much anyone who knows me more than in passing will know that I'm a big Chan fan. Have been for years. Probably always will be. I know more about his past than is probably healthy to know about an utter stranger. I check his website every so often and see what he's been up to and what he's currently doing. I debate his movies and the techniques therein with other ardent fans. I know he's had highs and lows in his career and while he's had some great cinematic moments, he's made some absolute turkeys of films! Particularly recently. And I've been waiting for him to pull something good out of the bag again. Arguably, the metaphor is so far sound.
Now if, just supposing, if he had just made an awesome film that was making big waves in China, taking some awards there, and was nominated for a Best Picture Oscar, I would never expect anyone to come up to me and say "Congratulations on the Oscar nomination". It seems preposterous to me. What have I done to be congratulated on? If they did, I wouldn't deign to reply with "Thanks. We put a lot of work into that film and we deserved the nomination".
Why?
Because aside from being a fan the film was created for, I had NOTHING to do with the crafting of that film. Certainly not enough to be congratulated on and to use the language "Thanks" and "we" as if I had personal involvement.

Genuine question: How is it not arrogant and utterly absurd to say "we played well" instead of "they played well"?