Frankly, anyone who doesn't classify Brawl as a fighting game, isn't seeing the forest for the trees. The term "fighting game" isn't some sacred oath that only the worthy must be allowed in. There are subgenres in the fighting games, and though it is contrary to definition, the best way to describe these genres are:
Arcade - Brawl
Sim - Tekken
(And don't get confused. Just because the sim subgenre got its start in video-arcades, doesn't mean the classification of Brawl as an "arcade" fighter is wrong. Fast paced and entertaining describes Brawl, while Tekken is a methodical defensive masterpiece of a series.)
Anyone who likes to kid themselves that SC isn't as much of a buttonmasher as a sim can get, is kidding themselves. I love how people always claim superiority at SC when the game has nearly no depth.
As for Brawl, the "arcade" subgenre isn't based on depth. Most people who hate Nintendo and have only played Melee for about 4 hours, don't realize it, but Smash Brothers has more available depth than Tekken, and SC is laughable by comparison.
You can't simply win over a buttonmasher on Brawl unless you are massively skilled and knowledgable with tactics and ring positioning.
The simple fact is, to master Smash Brothers, it takes far longer and much more skill than to master equivelant Sim games. I can testify to this myself, as I am a legitimate Tekken master.
I can't exactly prove my skills through a message forum, however I will say this. If you were in person with me, and played me in Tekken or Soul Calibur, you would take my opinions a lot more seriously than most peoples you know.
I can, however, offer up a shred of proof as to how deep Brawl is. Before you judge me to be an arrogant prick, I want you to watch this video:
http://youtube.com/watch?v=IqgrKz_N5G4
Now, watch the careful edgework here. Its easier to equate the depth of Brawl in your mind to the element of Ring-Out in Soul Calibur, however multiply that element by a factor of 10. See how, this player blocks off the center of the ring, the "safe spots" which never allows for the toe to toe confrontation his opponents are seeking, but instead keeps to the air to land his edge finishers.
Towards the end of the video, we see some really sick mid air smash to edge grabs, which boarder on psychic.
Now, 2 masters at these techniques will be an amazing fight.
So many people believe that Brawl, because of its frantic pace, is inevitably shallow, however there is a depth there that isn't apparent at first glance, and it takes longer, or perhaps, is impossible to master, compared to its fighting counterparts.
Either way, in the end, Brawl, for at least classification purposes, is a fighting game. What else is it? An adventure game, or a platformer? No, fighting, and a deep fighter too boot. Deal with it. At its core much more has been invested into the development of this game than equivelant fantastic, but still rehash franchises of recent memory.
imho.