Wherever the majority is allowed to rule unchecked, we do not have genuine democracy. This is because democracy does not simply consist of popular sovereignty or the rule of the majority. Instead, democracy must also include the protection of the rights and equality of minorities whether they be racial, sexual, political or of any other sort.
When the majority can rule unchecked, it can easily trample on the rights of minorities. We saw this during the Jim Crow era, for example, and we saw it during the McCarthy Era. One can argue that we see it now with respect to gay rights (depending on your point of view). When the majority rules in such a way, it takes away the rights of the minorities in a way that makes it impossible for us to have a fully genuine democracy.
Whenever the majority (no matter how large it is or how strongly it feels) is allowed to trample on minority rights, we cannot say that we have a system that is completely democratic.