Thank you all for your messages.

I feel better after reading what you all had to say. I also called AA again for a peace of mind. As bjtaylor said, one can't cancel a reservation without logging in the AAdvantage account. All this time, I was looking at my reservation from my account and I got all worried because all the options to change and cancel were available. But, knowing that cancelling a reservation requires one extra step of verification makes me feel much better.