You are right, the authors of the paper only claim that their results demonstrate a); they are, however, assuming b) based on previous studies.
What the Professor is arguing, as I understand it, is that those previous studies do not necessarily warrant the assumption of b), and thus the paper's title "A female Viking warrior confirmed by genomics" is misleading -- there has been a confirmation of "female", but not of "warrior". Something like "Skeleton, that some evidence points to being that of a warrior, was confirmed to be female"; but that's not as pithy or sensationalist.
Those not reading the paper sufficiently carefully (or at all -- only limiting themselves to the title and the abstract) will end up drawing conclusions unjustified by the paper. Which, given the political implications, may be undesirable.
What the Professor is arguing, as I understand it, is that those previous studies do not necessarily warrant the assumption of b), and thus the paper's title "A female Viking warrior confirmed by genomics" is misleading -- there has been a confirmation of "female", but not of "warrior". Something like "Skeleton, that some evidence points to being that of a warrior, was confirmed to be female"; but that's not as pithy or sensationalist.
Those not reading the paper sufficiently carefully (or at all -- only limiting themselves to the title and the abstract) will end up drawing conclusions unjustified by the paper. Which, given the political implications, may be undesirable.
[edit: grammar]