Averaging the samples can get you better accuracy... but how well that works and how long it takes depends on which errors you want to get rid of. There are three main categories of things which negatively impact GPS accuracy. They are noise, ionospheric distortion, and dilution of precision. Ionospheric distortion is what happens when the GPS radio signals pass through the ionosphere, and how severe it is depends on time of day, solar activity, and all the rest of the things that affect RF propagation through the ionosphere. Dilution of precision is the effect of less than ideal number and/or orientation of visible satellites.
Noise can of course be filtered out through averaging on short time scales. Ionospheric distortion and dilution of precision have long periods -- averaging them out entirely can take quite a long while. OTOH, the relative error those produce over small time scales tends to be small.There are other ways around those problems, like differential GPS, but they tend to be spendy.
And on the roboflyers thing: I think they're using GPS not just for position, but for orientation. It turns out that with 4 GPS antennae you can compare the phase of arriving signals at each antenna in a way that gives you an absolute position reference in earth-fixed coordinates. Like an IMU with no drift.