As a Nevada resident (hopefully soon to be Tennessee resident), I've gotta speak up on this one.
It's simply not true. There is no law in Nevada that prohibits carry in banks. The banks may tell you this, but they're full of crap wrong. I regularly carry in my bank (both open and concealed), even though they have signs on the door.
In Nevada, the sign at a private business means absolutely nothing. If they ask you to leave, then it's either leave or be trespassed. No gun law is involved, only trespass law. And this goes for any business where carry is not specifically prohibited by law, such as airport secure areas, schools, licensed childcare facilities, etc.
Public buildings (read: government buildings) are different. They can prohibit concealed carry by posting signs and/or metal detectors at all doors, and it must be at ALL public doors to be legal. This does not apply to open carry, since that law only applies to concealed carry. Many on the opencarry.org board open carry at the NV DMV with no issues.
The banks in NV may think that they're considered a public building, since they're open to the public. In NV law, "Public Building" refers only to buildings being used by the government, for government business.