The traction battery control module (TBCM) should have sent a message (DTC) to the PCM. If a fan or cooling system component was bad, the TBCM can stop charging and discharging with the PCM. Since Greg did not indicate seeing a Charging System Warning, but these other warnings:

"I can tell you what happened.. The vehicle would start,, I would put it into reverse, and the ICE would die. I would start getting errors on the display. It would say drivers door ajar, passenger door ajar, etc.... even service 4x4 soon, then it would say to come to a safe stop. At that point all would go dead... It would do this everytime...."

My thoughts are that the PCM had the error. The reason being that the PCM was receiving door ajar and service 4X4 soon and sending those messages as warnings.
I would be a little upset after they replaced the battery (two weeks) and then found out it was the PCM. After all, if the PCM indicated incorrect messages on the dash, the techs may have found incorrect TBCM DTC's. All guess work on my part.

GaryG