Well... they have a point to some extent. For instance, the 1st Amendment has nothing to do with states. According to it, your state legislature can restrict as much free speech as it wants to (although many states have constitutions reflecting a lot of the US Constitution, including free speech), just as some states initially had state religions (sort of). In that way, religious values could be taught in schools, and it was in no way a violation of the 1st Amendment because it was run by the state and not the federal government. At least that's how it's
written...
The way it is currently
applied , however, is through the all-encompassing, ever expanding
14th Amendment, which requires that rights be extended to all citizens (in its intent, of course, it was referring to freed slaves). This Amendment has been used to justify basically anything, but some may (and most do) argue that it does require at least certain parts of the Bill of Rights to be extended to the states, such as the 2nd Amendment (just as the 8th Amendment was used to strike down Louisiana's child-rapist-execution law).
As to being bound by the Constitution, yeah a state is bound to it... But like what was said, the Constitution specifically restricts
federal activity. So besides the things that the 14th Amendment would imply (which, yes, would include the 2nd Amendment), there is little else to be "bound" by.
On a separate note, would this decision have any implication on carrying weapons on base? It seems like a federal institution, especially when people live on it, would have to be bound to the 2nd Amendment. I understand Constitutional Rights don't always apply and the UCMJ takes precedent, but I guess I don't see why it's forbidden.