Most (almost all) genuine handmade Native American pieces do not have an open back. However, that doesn’t mean that if a piece does have an open back that it’s automatically machine made, mass produced, or “fake.” It may be, or it may just not be Native American, and not trying to be Native American. I think that the pieces that you posted probably weren’t made to intentionally deceive as Native American. Part of the issue is that some buyers and sellers just assume that many silver jewelry items with semi-precious stones and a certain look are Native American, even if they aren’t. Then once those items hit the secondary market it gets all muddled up, either by sellers who don’t know what they’re selling or buyers who are making an incorrect assumption. Of course there are plenty of fake Native American items that were made and originally marketed with an intent to deceive; I just don’t think these particular items fall into that category. They may still be costume jewelry; the one ring in particular looks like the band is not precious metal.
I have heard of NA artists using open backs on rare occasions, in the context of a translucent non-traditional stone such as amethyst, which really needs to let some light through to be shown off to proper effect.