1.) Technically she is part of the god-king lineage, as she married Vasher, who gave the god-kings their breath horde, but I don't think that's the reason.
2.) I believe it says somewhere or other that most of the knowledge regarding the events before the manywar was lost, so I assume that scholars of Nalthis' investiture simply aren't aware of the five scholars and the massive amounts of breaths they held.
3.) Even if 2.) is false, Vasher assisted in the creation of Nightblood, so even if she didn't possess enough breaths, Vasher could have lent her some.