Actually the capacitor does add a filtering effect, look at the signal with a frequency spectrum analyzer (aka FFT). There will be less noise over the frequency spectrum due to less and/or smaller spikes in voltage. The cap accomplishes this filtering by quickly storing and releasing small amounts of charge, and it is frequency dependent.

The cap does need to be in a circuit to act as a filter, yes, but it is in a circuit once plugged into the receiver. The circuit typically includes the BEC power source which has an output impedance (complex resistance) and the receiver & servo which have input impedances (same).

There are many types of filter circuits, one of the simplest is oddly enough a RC circuit, Resistance-Capacitance. Google will find this quite easily, one of many examples:

Wikipedia - RC circuit