They are referring to noise coming from either the charger or load. The filter stops high frequencies from affecting the voltage reading at BAT, which could otherwise cause switching of the cout or dout when you don't really want it. By sharp negative transient, imagine what happens when you connect a load that may take a lot of inrush current, thus dropping the voltage very quickly. The FET would turn off and you would not get a clean startup. The resistor is part of the filter. Not much current ever flows into the BAT terminal as it is just the input to a pair of comparators, which will be very high impedance.