You "think" you dropped it once? You "probably" dropped it?
How can you not be 100% sure if you've ever dropped it or not? If I dropped my ~$1500 laptop, I would remember the time and the date and it would have haunted me for weeks until I was sure my MacBook was damaged or not. Every time I would look at the "small crack above the drive where like, part of the keyboard edge is gone", I would have flashbacks.
Sorry dude, but something with your story isn't adding up, and you're looking to this forum for justification against the Apple Tech Guy's decision
(Sorry, I just don't like calling them 'Geniuses'. If they're geniuses, then I guess I'm a super-genius, since on many occasions I've ended up knowing more than them when I've brought my Mac issues to them. And I don't think I'm a super-genius.

).
I think you know exactly how you damaged your MacBook, and you're looking to this forum for ways to get it fixed for free. Which is fine, but just be honest- tell us exactly what happened to your MacBook, and people here will try to give you helpful advice on how to take advantage of AppleCare.
If I'm way off, I apologize, but your story is just, well, not believable.