Write them anyway. I’ve had that BS, usually from USPS or UPS Mail Innovations (which is horrific service), and a quick email to CS gets me the credit (money or a month of Prime).
I think it depends who reviews the complaints. Every single time I've responded, my complaint (which I always word calmly, non-aggressively, and politely) are met with the response that "2-day shipping only guarantees that the package ships to your nearest Amazon warehouse within 2 days. The actual delivery time can vary, and while it is typical that the delivery will arrive on the same day it arrives at the warehouse, there's no guarantee." And nothing more. Well, one time I was offered a $5 credit. But that's the most I've ever been offered.
At this point I already cancelled my prime with Amazon, and generally try to buy things from other sites if possible. The counterfeit issue alone makes me avoid them whenever possible.
