I can't figure out what, from the parent's comments, would make you draw this conclusion that it is a people skill problem when it sounds like a classic "whiteboard interviews are a total crap shoot" problem.

This experience is not even at odds with the original quote from the recruiter - when the recruiter says "qualified", all they mean is "able to succeed in the hiring process companies are using". Unfortunately, that definition of "qualified" often doesn't have much in common with the usual definition of "capable of doing good work". The parent commenter may well be qualified in the second way but not in the first.