Here's an update...

To refresh, the tech earlier said I was opening the doors/tailgate/hood to much and ran down the battery, and it just needed a recharge. I insisted they test the battery, while the tech was adamant that there was nothing wrong and I was opening things too much.

Here's what the tech later wrote on the invoice after completing the service:

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Checked fault code memory and performed energy diagnosis. Energy diagnosis says to recharge battery, however tester states to replace battery.
Performed battery test. Battery failed.
Replaced vehicle battery and left feedback to BMW to correct test plan.
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After putting the new battery in, the tech tried to reprogram for the AGM battery (black case from original white case.) It wouldn't complete programming and indicated the tailgate module was defective (remember, I brought it it with a non-functioning tailgate as well). Tech wrote on invoice:

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"Found HKL submerged in water while inspecting wiring."
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Water tested and determined leak was likely due to manufacturing flaw in trunk lid gasket. Replaced module and truck lid gasket.

Tech says earlier information about locking and unlocking too often likely false information caused by HKL module being submerged in water and sending false signals/not going to sleep, e.g., vehicle may have been unlocking and locking rear hatch while parked or simply sending signals keep vehicle awake.

So two conclusions: (1) I guess I wasn't sitting on my keys on the couch.... and (2) blindly believing the vehicle computer over the customer's information isn't always the correct course of action.