I agree with that, I think the crucial difference is that some men are weak and their partner compels them into a position they didn't want to be in (sharing his wife). That is wholly negative and not "alpha".
My perspective is that a man who truly, genuinely, is not threatened and can find enjoyment in his wife exploring other partners is not a beta. This is happening according to his will, not the other way around. Sure, some of those guys are frauds and are deluding themselves but at a certain point we have to take people at face value. If lindz is describing this dynamic accurately, and if her and her husband are communicating accurately, then I wouldn't think this guy is a beta.