I think the appeals overturn councils relatively often.
Really? I would assume from the context you are referring to lds disciplinary councils, is that correct? I would be interested why you think these councils are overturned "relatively often."
LOl Relatively often is a very subjective language. What he means by relatively often could reasonably be viewed by others as hardly ever. I suspect though he has no actual data, but is offering an ignorant opinion on something we are all ignorant about.
If I recall correctly, the letter Natasha received said she could appeal on grounds of procedural error or unfairness in the process. She puts forward plenty of evidence about that, starting with the conflict of interest the stake president has, being the employee of her ex-husband.
Evidence and rules mean nothing here. There are no enforceable rules when it comes to membership in a religion. I would not be surprised if there are 0-2 successful appeals in the last 50 years.