Whether or not they can afford a bottom quartile home is a different question than whether it's reasonable to expect them to afford a median home (and I don't think we have any evidence regarding that question here). They certainly aren't expected to be able to afford a top quartile home, for example, so I agree that the headline is a bit fishy.

The whole situation is being drastically oversimplified, though. Whether or not we expect minimum wage to support a family depends on whether there are other alternatives, like higher (and adequate) wage jobs that individuals can reasonably obtain when they do have to support a family. Is that happening? My sense is no -- we have a big step function where you're either mostly screwed (working several jobs, driving Uber, etc. barely making it if at all), or you're making 6 figures after getting a 4 year degree in some technical or professional field.