The GPS precision thing might be beaten to death, but I have a couple comments:
(1) Most DGPS antennas actually have "blinders" installed on their antennas to prevent them from seeing satellites near the horizon, as the psuedorange seen through that much atmosphere is suspect. As such, an aircraft-based system is bound to be less certain, especially since it can't guarantee the orientation of its antenna.
(2) The most common source of wandering GPS positions is Geometric Dilution Of Precision (GDOP), basically the randomly spaced satellites line up in such a way that the intersection of their spheres contains a relatively large degree of uncertainty. One the plus side, these are much more predictable, and measurable, than solar flares, see:
http://en.wikipedia.org/wiki/Dilution_of_precision_(GPS) and the link at the bottom of the page
I suspect that similar algorithms will chose the same position given the same region of possible solutions, but that can't be guaranteed. If one's Bloxes "wander" together, that's probably what's happening.
Final thought: It might be interesting to see if it's possible to improve the navigation solution by either tying the measurement covariance in the EKF to the system's reported GDOP (I'm not volunteering to that) or otherwise discounting the GPS measurement when the satellites are poorly aligned. Actually, there's probably a really cool paper, maybe a dissertation, in investigating that problem fully (and I already have a topic).