Their point is still wrong, though. Their argument is purely against existing historical applications of Marxism-Leninism, not on the actual structures of Communism, nor what Communists believe.
Many Democratic Socialists are simply Communists that think society can be meaningfully reformed into Socialism, rather than revolution. All suggested forms of Communism are democratic to their core, that’s the underlying philosophy behind Communism.
The nuances are in historical applications of Vanguard parties, which tended on the authoritarian side, with flawed implementations of Democratic Centralism. Throwing the entire baby out with the bathwater, rather than attempting to address the system of Democratic Centralism and other structural flaws present in the USSR for example, is flawed thinking.
Liberal Democracy, as is the usual form presented by Democratic Socialists, is less Democratic than forms such as Council Communism, for example. There’s legitimate discussion to be had, Liberal Democracy being a requirement for Democracy touches on the subject of Capitalist Realism, by which the presence of Capitalism entrenches a sense of permanence on those living in it, even if unfounded.