(best "ancient aliens TV series voice) Perhaps it MAY be that what ever is causing the lifting, is causing a load on the battery as soon as it is plugged in, and this giving a bad voltage reading to the BDI circuit. also perhaps a defective connection or spring in the battery connectors causing a voltage loss.
is it possible to swap out this battery into another unit for testing? or plug a different (same nominal operational voltage) truck into this battery? can you take voltage readings right at the battery cable connections? ?