Yeah, I can hear it that way too. Thanks for sharing your interpretation.
I guess I'm not so triggered because it looks like the movement is towards change from the current system rather than violently overthrowing it. I hear it as "the current capitalism is bad", somewhere she calls it industrial capitalism. "People can't afford a house over their heads" sounds to me like a goal to make that happen. Perhaps she has a different view on what afford means than I do because it indeed doesn't need to mean possess.
In today's sensationalist tendencies I half expect people to make quite extreme statements to express even the smallest desire for change.