The more you think about it, the more you can argue that Max Payne - and quite a few other action games - are greatly exaggerated stream of events. But in the direct case of Max Payne, there's a strong chance that it was Max himself doing the exaggeration.
Throughout the Max Payne series, the lead character narrates a good portion of the events that unfold; either through comic-strips between chapters or as you reach key moments and decisive opportunities.
In a recent interview with VentureBeat at GamesLab in Barcelona, however, Max Payne creator (and likeness) explained that what we achieved in the game wasn't necessarily how it really happened.
"... Because we had such a strong main character, the whole experience is his version of events. Max Payne tells the story, narrates it. To me, that always means you’re not actually playing how it really happened. You’re playing how Max tells you how it went. All of those TV shows, all that transmedia material, seems to be commenting on his journey and his character. Is that really what’s happening, or just Max’s perception?"
Did Max just like to add that extra spice of drama to his story of love, loss and vengeance? Or did drowning his sorrows in drink just cloud his perception of what took place? He did go on one hell of a killing spree - and some rather trippy dream sequences.