One factor no one is considering is rust. The years 1765 to 1850 were in the blackpowder era. Blackpowder soot is highly corrosive to the iron gun barrels used then. The rust inhibiting oils we now have were also not available then. Combine that with the primitive state of iron working (brittle or soft parts), and the fact is that guns did not last that long back then. The assumption in the study is that a gun would always be a highly valued inheritance, when it more likely was considered rusted, worn out junk, with maybe some sentimental value.
Most of the population back then were farmers. On reaching adulthood the farmers children would usually move away to frontier land (which was cheap to buy), and set up their own farm on land that wasn't worn out. It seems common sense that they would have their own gun at that point and wouldn't need dad's old musket.
During the same era, on the other side of the continent, mountain men were trapping furs in the Rocky Mountains. They would go off in the wilderness for a year to trap, then meet at the big annual rendezvous to trade. The standard pattern was to buy a new rifle at the rendezvous, use it for a year until it was rusted out, sell it to the Indians, then buy a new one for the next year's use. The world's best and toughest (Hawkin's) rifles would only stand up to a year's hard use back then.
It seems to me that Bellesiles is guilty of assuming 1800s American culture was like modern American culture combined with assuming 1800s gun durability was like modern gun durability to indirectly infer who owned guns. I think he is way off.
Al Germain