Most if not all DC/DC chargers that I have investigated will go into float with a LA or AGM battery once the auxiliary battery is fully charged and turn of if a Lithium battery is fully charged.If you connect a charger to your starter battery without disconnecting the auxiliary battery, you may inadvertently flatten the starter battery.
So you would have to have either a flat auxiliary battery for this to happen or a very small charger.
BTW many DC/Dc chargers have an ignition feed .
I call Fake News.
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