Look. Smash, be it brawl or melee, differs from the description and standards that a traditional fighting game adheres to.
Does that make it any less of a game? No. Nobody's arguing that. But to classify it with games like Street Fighter and Tekken is wrong. In my mind, Smash if far more strategic than a traditional fighting game. It relies on the player to concentrate far more on their positioning, vertically and horizontally, in relation to their opponent, and in that regard, allows for for more options both defensively and offensively that the player has to know and understand.
Do the characters "fight"? Well sure they do, I guess that's where people say "clearly it's a fighting game", but we need to make the distinction between our beloved games and the "Traditional style fighters". You could almost call Smash a fighting/strategy/platformer/beat 'em up.