A lot of people believe that, Jim - but it's not true.
Listing a building on the National Register of Historic Places carries no weight whatsoever with regard to demolition, or even remodeling for that matter. It it simply a ceremonial designation.
The worst "punishment" that can be meted out to someone who moves, alters or demolishes a listed building is that its listing can be revoked. That's not exactly a deterrent to someone planning to tear down a building.
All you have to do is open up any copy of the National Trust for Historic Preservation's magazine to get a monthly dose of historic, listed buildings being destroyed or irrevocably altered.
Local historic district designations are often designed specifically to protect old buildings, however.
JAC