Battery Math

I purchased a portable compressor to inflate the various funspheres at the camporee and went to return in as after spending some time charging it wasn’t yet showing a charge.  The return was, tough.

Me: I’d like to return this compressor, it’s not charging.
Salesperson: They tend to take a while to charge, are you sure it charged long enough?
Me: Yes, it’s been charging for 72 hours.
Salesperson: Well, it can take almost a day.  Are you sure it charged long enough?
Me: That’s three days.
Salesperson: It is possible to charge it too much, have you discharged it at all?
Me: *waits a moment* Please, just let me return it.
Salesperson: Ok.

I enjoy the impossibility of the ssalesperson’s penultimate statement.  If it couldn’t be discharged because it was overcharged, how would I discharge it?  Also, how could you overcharge a battery to the point where the device showed it needed to be charged?  I would love to meet the vengeful engineer who designed a battery that operated like a Super Mario Bros 2 where if you went off one side you’d appear on the other.  You’d just let the battery continually charge and either time it to disconnect it at the right time or play a wonderful game of roulette with your emergency compressor.  Will it work?  Will it charge?  No one knows!