I suppose if you are pedantic, "There Ain't No Open Bottle Law in Texas" being a double negative, on a strict interpretation it means there is an Open Bottle Law in Texas. Which appears to be the case. Whether that observation is any help, I rather doubt. My impression is that, generally, country musicians are not particularly noted for their pedantry.
I note from Jim Dixon's link that it's not just open bottles - it's illegal for a passenger to have a closed bottle too, if it has has been previously opened. Good grief!