There really isn't much to argue about here. AA's service plan is quite clear, e.g. 24 hours from ticket purchase. The fact that some people have been able to exceed the 24 hours is no different than the fact that some people manage to have a change fee or other condition waived. The bottom line is that if you cancel after 24 hours, you should plan on being held to the fare rules, be pleased if you are not, and accepting if you are.

"When you buy a ticket 2 or more days prior to departure via aa.com or by phone with American Airlines Reservations for American Airlines flights (including American Airlines flights operated by codeshare partners), you have up to 24 hours from the time of ticket purchase to receive a full refund for your ticket.... After 24 hours have elapsed, normal refund policies apply to the ticket. If you elect to make changes to the itinerary after the 24 hour time period, a change fee may apply and the ticket price may also change depending on the fare purchased."