There are two types of giveaways as far as The Well Dressed Sports Fan is concerned. The first falls under the category of "free stuff to give to your nephew or Dad". The second type of giveaway occurs only during special games - playoff baseball and basketball and rivalry college games. In the above picture, Penn State has successfully accomplished a "white out" effect. The Golden State Warriors, during a recent playoff run, gave out bright gold t-shirts that read, "We Believe".
In the second kind of instance, it is just fine to throw on the oversized t-shirt. What the hell, right? Go for it. The effect only works if everyone is doing it and you don't want to be the tool that decides at that very moment they've never been a sheep in their life and they refuse to play along.
In the first example, limited free shirt, hat, or trinket giveaway - just pocket the damn thing and worry about it later.