I'm not up to date with the racial arguments you mention. I know there was something of an obsession 50-100 years ago with trying to establish a scientific basis to justify racism, imperialism, land theft, sterilization, imprisonment and subjugation of non-european peoples and there are still vestiges of those assumptions in a lot of research.
With the claim that "individuals from two different races, for example Caucasian and West African, are usually more similar genetically to some members of the other race than to some of his own", I have heard similar claims but how I understand it is they are not saying randomly chosen individuals from two different groups are more similar than randomly chosen individuals from within a group, but are comparing diversity of individuals within a group to diversity of group averages between groups. In other words, the claim is that the variation between two related individuals is greater than the variation between two unrelated groups, taken as averages. You are correct that if the claim is being presented that individuals between unrelated groups are more related than individuals within related groups, the argument doesn't make sense. It would not be surprising though if it has been presented that way in some articles and then repeated until it became a self-propagating myth. And again to clarify, I'm not up to date with any of those arguments, but just speculating on what might be going on.
I'm not arguing any position, just trying to understand without being very familiar with genetics or statistics. Maybe I've read the studies the way you presented it but my simple mind interpreted it that way. I'm guessing there is a huge flaw in what I drew but I don't see it, I can't picture in my mind what you meant.