Another, methinks more obvious explanation, is a reverse causal relation - people who own fire arms tend to mistrust the gov't (rather than those who mistrust are more likely to own). A possible reason for that is the KKK mentality ("I can shoot any minority person I want") which the fed curbed a bit during 1960s. Hence the KKK crowd who tends own guns also tends to mistrust the fed for its opposition to lynch mob violence.
In the same vein, black "gangstas" who tend to own guns are also likely to mistrust the gov't who they see as a symbol of "white man's power."
Third, gun ownership often implies participation in certain types of social circles frequented by militia types who are paranoid of the gov't and thus affect the views of other participants.
In other words, being determines consciousness, behavior (ownership) affects ideology (mistrust), not the other way around.
PS. Did the researchers control for being a redneck? (education is NOT a redneck status indicator).
wojtek