From what I know, steam looks solely at your licenses. If you have the license to the game in your account, it will (or should) be included.
So it looks at neither your library or your history.
Your example is a bit odd though, not sure I can explain that.
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You know when you buy some games, such as COD Black Ops 2, you get the singleplayer, multiplayer and zombie mode? For some reason the number of friends who played the game seems to be different even though they all thereotically own the games.
So I'm guessing Steam looks at your play history rather than your library? Doesn't make that much sense to me since free weekend would also be counted.
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