Guess the obvious question is whether it's a problem of A] sensing battery voltage or B] a charger problem, or C] the battery itself. The indicator may in fact be correct. The problem is most likely B or C.
If you try to operate it without an external power source, about how many minutes will it run before shutting itself down due to lack of battery? That XL One has a few years on the battery by now. Then again, if it's not charging well due to the charger, we can't blame the battery, can we?
Is there any difference in the indication when you have had the unit plugged into the car charger vs. your PC or mains charger at home?