As is usual, when these people are in front of an audience that they perceive as friendly, they are more honest than they'd otherwise be.
And Hugo Chavez is not alone in this belief. Let's start with Woodrow Wilson.
"it is very clear that in fundamental theory socialism and democracy are almost if not quite one and the same"
("Socialism And Democracy", 1887)
Occupy Wall Street:
"The only way to have a genuinely democratic society would also be to abolish capitalism in this state"
(Occupy Strategy Session, March 2012)
"The struggle for self-determination has had two stages : (1 ) a united front against imperialism and for New Democracy (which is a joint dictatorship of anti-colonial classes led by the proletariat, the content of which a compromise between the interests of the proletariat and nationalist peasants , petit bourgeoisie and national bourgeoisie) ; and ( 2) developing out of the new democratic stage, socialism."
(You Don't Need A Weatherman To Know Which Way The Wind Blows, 1969.)
Van Jones/STORM Manifesto
"Like all effective organizations, STORM had to figure out how to support leadership while fostering democracy."
The manifesto "Reclaiming Revolution" is one of those which I recorded as an audiobook. If you want to understand Jones and the left, this manifesto is a great place to start. If you can't make time to read it, then you have the option listen to it. The STORM manifesto uses "Democracy" or "Democratic" 42 times.
And finally, the Fabian Society.
"She (Greece) fell before a united Macedon, even as Macedon fell before the larger unity of the Roman Empire. But did they not try a virtual Socialism in Athens? And while it endured, did it not produce an individuality elsewhere unequaled in the world?"
(William Dwight Porter Bliss, Founder of the American Branch of the Fabian Society. "Where Socialism was Tried" - November 11th, 1905.) In case you don't go read the article, he is indeed pointing to the birthplace proper of Democracy as his proof that Socialism has been tried. Athens, Greece.
The left's active definition of the word "Democracy" is "Socialism", and it has been for a very long time. They'll never announce it openly enough to make it into a dictionary,(or at least, every dictionary I've seen treats democracy and socialism as separate items) but it's pretty set in stone for me. They use a different language than we do and it's important to understand their language, if you truely want to stop them.