It does sound like you were not a "culture" fit for Amazon. But why tie your self-esteem to a company like Amazon? They have had been called out over the last couple of years for their hiring and work culture. I doubt that they've resolved all of that at this point in time. It's not you. Quite frankly, you could probably find a better company to do this type of work for.

Regarding secrecy - companies of Amazon's size are by the book and always concerned about any potential legal liabilities with regard to HR. The rule is usually "say as little as possible". This is pretty much the case everywhere today.