The current incarnation of the question merely asks if there is evidence to support the claim of a gender pay gap in nurses in the USA.
This is easily demonstrated as the article provides a link to a study published as a Research Letter in the Journal of the American Medical Association:
The study looked at two large longitudinal surveys (one from 1988-2008, the other from 2001-2013). As reported, in more recent one, the 10% male figure is correct (20,616 men of 205,825 Registered Nurses).
As reported, the gender pay gap accounted for a little over $5,000 p.a. and hasn't changed over a twenty year period. (Note: that period ended in 2008, not 2013.)
Both surveys showed that the unadjusted male salaries were higher than female salaries during every year. [...] No statistically significant changes in female vs male salary were found over time. Using the [older survey], regression analysis estimated an overall adjusted earnings difference of $5148 (P < .001)
Confounding factors they considered for the regression analysis include:
demographic factors, work hours, experience, work setting, clinical speciality, job position, survey year, state of residence and other factors.
So, the quoted excerpts in the USA Today newspaper article are backed by the referenced journal article.