Yes, the “just build houses” contingent seems unaware that people (and as Mitt Romney famously said, “corporations are people too”) can own more than one house. Supply is certainly an issue, but inequality is as well.
I don’t remember the context that well, so you may be correct about that, but I think I disagree with him then - I think corporations are made of humans, but they are machines (perhaps primitive AIs) and are as uncaring as a lawnmower.
Every time a mob of people get together responsibility becomes diffuse. You may see a corporation do something negative that was the cumulative result of 100 human beings who thought they were doing what they were supposed to. People who saw themselves as not able to directly control the outcome. Same for any large group of people up to and including nations.
