that's an example, yeah.
intuitively, you know a battery provides power and a resistor absorbs/dissipates it. at the POSITIVE end of the battery, current flows out. at the POSITIVE end of the resistor, current flows in. it's just a simple matter of associating those two points.
And yes, when a battery is being charged, current is flowing INTO the positive end, so it is absorbing power instead of sourcing it.
using positive and negative power is sort of a convention, so it depends on the context whether you use that or just always positive and denote whether it's sourcing or dissipating power.