Yes, it's true, they probably would not have cared as much if we weren't using their name and referring to their logo. But ultimately we were a service that sold Amazon gift cards, so it was always going to be up to them if they wanted to let us continue to exist or not. We decided to give it a shot and see what happened.
I really don't think you understand how trademarks work.
If you willingly let your trademark be diluted, you will lose control over it. Amazon had absolutely no choice about shutting you down. That they shut you down was a completely foregone conclusion from the start. It's not about whether they mind what you are doing or not, it's about whether they lose exclusive access to their trademark. Had they not shut you down, and let you run for long enough, anyone could have used your existence as a point in their favor at court when arguing about using the Amazon name.
I'd say that there were probably better ways to make this clear.
Soooo yeah, companies have things called "trademarks" and "copyrights"... you can't just go putting another company's name inside your company's name, and then make your imagery the same as theirs, without their lawyers sending you a strongly worded C&D. However I don't see why this would have to shut down based on that -- why not restart under a new, distinct name and branding?