We had almost the exact thing happen to us, at a local tire dealer. He tried to get out of fixing/repairing what we knew was a defective tire.
Call BF Goodrich’s customer service department. Let them know all the things you’ve posted here (pop, rear tire vs front, if it were a puncture wouldn’t it a) be visible/have evidence of some sort and b) tend to leak over time). Also, let them know you see this as a SAFETY issue and that you’d not of expected this from their tire. It doesn’t hurt to try.
Good luck.
Thank you, I am going to call them!!