You're referring to frequentist/empirical probability there. But classical probability states that each individual event has the same chance of occuring, always. Which is what I assume what the system is built upon. Saying that "to get odds in your favor" you need to fail 28 times in a row is stupid, plenty of people have gone WAY over 200 consecutive FATEs without a single atma drop; and please don't tell me that these people have NOT gotten their Atma (with an 8% chance of failure, which is constantly decreasing according to empirical probability) 100 FATEs after the first hundred.
I'm just going assume that the Atma drop works this way: You have a certain chance (say 5%) of getting an Atma after finishing a fate with gold rating. If you got it, then that means that the 5% worked in your favor. If you didn't, then that means that the 95% chance of failure made you not get the drop. Also, previously completed FATEs, with unsuccessful results, DON'T affect in any way your overall chance of getting an Atma drop in the future.