Not being a individual's concept of "proper democracy" does not prevent a government from being a actual democracy in fact. Most democracies today (and through history) impose at least some restrictions upon who is a eligible voter.
In terms of personal perspectives of what constitutes a proper democracy, my personal view that we should have citizen's initiatives at the federal level, as we do at the state level, doesn't prevent America from being a democracy.
The governmental system isn't perfect, and likely it never will be. Still a democracy.
(Not just you, but everyone else)
America, Britain, etc, are not democracies. They are republics. America's system of government in particular was set up to prevent a democracy, as democracies invariably turn to the tyranny by the many. A representative, however, can say no to their constituents, if the representative feels that what the people want is wrong. That may come back to bite them in the rear, true, but often the worst impulses are just that, impulses, and the issue dies down. (Also, it wasn't set up so that representatives make careers as politicians, but that's a whole 'nother issue.)