I am really sorry that you are frustrated and embarrassed. It must be such a bummer to get that kind of letter.
I will admit though, after reading the whole thread I had to go back and check if you were actually banned. I am another who is a little confused by the level of outrage and irritation.
The OP is not actually banned from much of anything, except that she must have a receipt when she returns. I think this is standard retail policy in many stores. She can still shop, she can still order, she can still purchase, she can still change her mind and take it back. She isn't getting charged for former returns or anything of the sort, nor was she prevented from making the returns. Coach (a corporation apparently plagued with shrinkage and reselling issues) notices that she is making not one, or two, or three, or four, or five....weird returns in a handful of months, and with no way of knowing her story, decides that okay, just to be safe, please be careful to bring a receipt. I don't consider that bad policy.
The issue is also being taken very personally. I agree that it is unfair and hurtful to be a loyal customer and feel accused. However, this is not an individual SA or manager who labeled a problem customer and suddenly barred your return. The decision came down from corporate headquarters, quite possibly automatically. No one on Coach's end is making a personal judgment, it is a business based decision to stop returns from possibly questionable sources. Being a frequent customer doesn't prove that someone is honest. Many regular customers probably DO bend legal and company regulations. Coach isn't being passive aggressive, they're a corporation and have no motive to be passive aggressive. They are saying exactly what they mean: these returns are questionable, and because six transactions in six months looks chronic, we need to ask that they stop.
Also, Coach provided an opportunity for her to call and speak with someone. Keep in mind that no one is going to call corporate and confess a life of crime. Whether she uses that number to have a fit or to explain her position, Coach handed her an appropriate outlet to further discuss the situation at her discretion.
I don't think it's ideal for a customer to have to get a warning letter, and I think it's so sad if they are someone honest and reliable. I sincerely hope it gets all straightened out. However, I don't understand the shock mentality, if nothing else.