gunnie I think you and rcmodel are talking past each other.
Yes, both the BAR and Thompson were available for civilian sales before 1934. But, as you've quoted, there wasn't much of a civilian market because the guns cost a whole lot of money and very few average citizens had any interest in an automatic rifle. Certainly not enough interest to spend the kind of money they cost.
If you think about it, a 1928 Thompson probably cost about as much in 1928 as a lower-valued one does now -- after the Hughes Amendment inflation. Nowadays there's a sizable hobbyist shooter population that will put large chunks of "disposable income" into such a thing. In the '20s-'30s, "disposable income" was not a common phenomenon.
I think what rcmodel was saying with "none were ever offered for sale to civilians" was that the military never sold surplus machine guns directly to civilians -- not that they weren't available through gun dealers or direct sales.
Of course, without the benefit of "surplus" rifle pricing, very few military weapons of any kind would have been purchased by civilians at any time. I paid $265 for my M1 Garand from the DCM just before the CMP arrived on the scene. No manufacturer could sell a complex and high-quality arm like that for so little. Sure there are millions of them (and 1903s and 1917s, and Mausers, and Enfields, and K-31s, and Mosins, etc., etc.) in civilian hands, but if they'd all been priced at "market value" instead of surplus/scrap prices, they'd mostly still be in government warehouses the world over.
No gov't surplus machine guns = very few machine guns ending up in civilian hands. Fast forward to 1986 and the government says, "YOU CAN'T," and all of a sudden everyone wants one and folks will pay $40,000 for a pristine Thompson with pedigree.