There's a bit of a problem of consistency in the conclusions proposed to try to debunk the myth. Watch carefully what Woods says and then, what Root says.
Stossel: There's a myth that unions built the middle class by increasing their wages.
Woods: Yes, it is an incorrect myth. Investment in capital increased productivity, allowing wages to rise.
Stossel: And they say unions were great equalizers for minorities.
Root: Right. This is incorrect. In fact, early on, federal laws, including the Davis Bacon Act made it illegal for non-union labor (basically, Blacks) to compete with union labor (Basically, Whites). Thus, Blacks could not compete by offering their labor, which was cheaper. Thus, Whites used unions to prop up their wage rates by using discrimination and anti-competition.
Woods and Root make inconsistent observations. Woods says wages were higher due to private market forces and capital investment. Root says wages were higher because of unionization. (Of course, I bet Root did not realize that's what he was saying, since he was really trying to paint unions as racist).
How to decide who is right? Any of them? One of them? Both of them (partially)?