As soon as I saw that picture I thought "manufacturing defect"... Being that this is you and your tire, it's highly unlikely any of your use (or alleged abuse) caused this failure.
Severely under-inflated, overheated, or overloaded since put into service? I doubt it, and I'm sure you know the answer.
It's nice Cooper is giving you a new tire, the only thing to do. When you wrote that all the tires are from the same lot, I thought the next thing you were going to type was that they were going to give you a new 'set', replacing them all. That would be ideal, but would cost them a few dollars.
As you know, the Cooper S/T MAXX is one stout tire with a very heavy-duty casing (like the Toyo M/T), but it just reinforces the fact that all tires are relatively fragile and soft and are sooner or later a disposable, wear item.
Glad you didn't have a wile ride at speed when it decided to separate.
Confirming, the casing/sidewall split but the tire still held air?
Thanks for the updates!
James