Actually, they are right. We are a republic that happens to use democracy to select our leaders. In a true democracy, it is pure majority rule. We have lots of restrictions that prevent the majority from enforcing its will over minorities. The whole separation of church and state, the Equal Rights Act, and many others all ensure that the majority cannot do anything and everything that it wishes. We are a republic first and and democracy second.
The distinction you are making between a representative democracy and a direct democracy is valid. But even our representatives have restrictions, so the rule of law (our constitution) trumps any vote. I don't know of any nation that is a true democracy, everyone seems to have gone down the republic path.
And remember that democracy cannot be used to change every bit of our constitution. For example, there is no mechanism to leave the United States of America. Just ask the Confederate States of America.
- doug