Not greater. Total control by workers or the state. They are anti-capitalist.
They are anti-capitalist as a matter of policy, yes. The definition of that is pretty muddied though. Most European social democrats, and even many Christian Democrats, would describe themselves as "anti-capitalist" by which they mean "anti-unfettered market" and "historically anti-corporate control - but within the bounds of what works given the horrors of state socialism." In the former case "has bottom-up workers' democracy sympathies but prefers an evolutionary path to it," in the latter case "has distributist/socially conservative workers' democracy sympathies but prefers an evolutionary path to it." I'm anti-capitalist in the latter sense, for example, and am a European conservative. The evolution of Christian Democracy/Red Toryism from distributism was a direct one.
DSA seems to, at tamest, be the former of those; evolutionary social democrats, whose outlook ultimately came out of the socialist workers' movement. It also seems to encompass state socialists, workers' democracy advocates who prefer a more revolutionary or violent path, and confused mixes of the three. In short, it seems like a wide swathe of people who want to pull the Democratic Party leftward, with various end goals. They're not a top-down organization, so they seem perfectly happy to have members of various stripes united under that common cause.
Her talking (PBS) was just icing on the cake.
I agree that her PBS interview was terrible, she's the prime example of polarization and kookiness not just being slanted to one party.