Except that I don't. I purposefully focus on my Destruction skill, in the form of casting as many Flare spells as I can, yet I never, ever come up as some sort of magic based character. While I do open locked chests, I'd be a fool not to, the only time I use Sneak is with that Goblin Shaman. With a Sneak Attack and the Damage Health potion I pick up, I can drop her with a single hit. And I only use my Blade if I happen to miss my target with my Flare spell. There's absolutely no reason why Bard show come up as consistently as it does.
Really? You're telling me that you use security, but that you think the results ought not to be taken into account just because you wanted what was inside the locked chests?
I'm telling you that it is possible to go through that tutorial acting like a mage, using only magic, and leaving the stuff in the locked chests. I've done it, and when I did it, Baurus correctly guessed "Mage."
One thing I'd point out, if you're hoping to spam a skill to influence being chosen as a magic class, the skill you'd want to spam is the Healing spell, which will count every time it's cast, since it always has a target. And, as it happens, if you don't sneak and wear armor in the tutorial, you are going to take a lot of damage, and get to use that skill quite often.
I'm not defending the game's method of choosing a "suggested class," because I agree that it's bogus (and I think I said so above.) But it's not "broken"; it actually works as it was designed to work. The method is silly, and the system used in earlier TES games was simpler and more to the point - just a series of questions whose answers led to the class suggestion. But it actually does work if you do the things it's looking for.
Most people are simply not playing the class they think they're playing. Think about it. You're a mage, and you just escaped from prison, and you're running through a rat-infested cave. You've already met one zombie, and you don't know if there's worse hiding in the next shadow. Are you really going to stop and spend precious time trying to teach yourself to pick locks, just so you can get a couple of gold coins and two lockpicks that are in there? No, you wouldn't. A Thief would, but a Mage wouldn't. A Mage doesn't need anything that's in any of those chests.