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It's weirdly phrased, but it just means that they don't have a tight control for battery capacity. Their device is designed to operate for at most ten hours (for example), but the battery that they use could have anywhere between 8-12 hours of supply, so the transmitter would be active anywhere between 8-10 hours.

In your scenario the device shuts done when the battery runs out, but at the latest after 10 hours. That's different from "at the latest when the battery capacity is exhausted".

Instead the implied mode of operation is that they shut down after 10 hours, but sometimes they dont and after 12 hours the battery is empty. Or maybe it's another trigger (location?) that is not always active or does not always trigger

They just have access to classified physics and definitions of energy most people don’t have.

Turns out the weather balloons are powered by swamp gas.

Small solar panel and a charge controller. Defeat physics with this one trick.

My transmitter shuts down after a certain amount of time. At the latest when the solar panel is heavily degraded. This is due, among other things, to strategic considerations