No, no, that's too simplistic of an analysis. It does indicate that there isn't egregious hiring bias, but the Berkeley survey I linked only shows a 10% bias. That's too small to reliably detect with bulk numbers because, for example, people can just eat the bias and send out more job applications or take a less desirable (lower wage) job. And we don't have a good way to measure whether there is a difference in need for or desire to have a job (e.g. although there are not many housewives these days, there are some, and that generally requires both marriage and a decently high-paying job, and that's not equally distributed across race either).

So you can't just look at the workforce and say, "Oh, no discrimination in hiring!" Just like you can't look at the number of tenured full professors of mathematics and go, "Oh, discrimination in hiring African American mathematics professors!"

The value of things like the Berkeley study is that it cuts through all the ambiguity and shows that when the only possible piece of information people have to go on is a highly racially-suggestive name, there is a bias. Otherwise you have to really dig into the details, do factor analysis, all the rest.

I haven't validated all of Erik's examples, but I checked out several and they seem decently solid (if not all completely inarguable).