I tend to prefer the white text for borderline cases too, but the plugin actually calculates whether higher visual contrast is achieved with white or black. If black provides higher contrast and white provides a contrast ratio that is below the 4.5:1 minimum required by the WCAG 2.0 guidelines, black is used.
The best way to override this behavior is probably with some custom CSS (via a custom CSS plugin). Just note that this would cause accessibility issues potentially.
This is the css to change the color back to white when the contrast color calculation leads to the color being changed to black:
.site-description,
.secondary-navigation a,
.widget,
.widget a,
.widget_calendar caption,
.site-header a,
.site-title a,
.site-title a:hover,
.menu-toggle:before,
.site-footer,
.site-footer a,
.featured-content a,
.featured-content .entry-meta,
.slider-direction-nav a:before,
.hentry .mejs-container .mejs-controls .mejs-time span,
.hentry .mejs-controls .mejs-button button {
color: #fff;
}
.slider-control-paging a:before {
background-color: rgba(255, 255, 255, .33);
}
.widget-title, .widget-title a {
color: #fff;
}
.secondary-navigation li {
border-color: rgba(255, 255, 255, .2);
}
.secondary-navigation {
border-color: rgba(255, 255, 255, .2);
}
.widget input,
.widget textarea {
background-color: rgba(255, 255, 255, .01);
border-color: rgba(255, 255, 255, .2);
color: #000;
}
.widget input:focus, .widget textarea:focus {
border-color: rgba(255, 255, 255, 0.4);
}
#supplementary + .site-info {
border-top: 1px solid rgba(255, 255, 255, 0.2);
}
(There is an additional set of CSS to override black text against the accent color, but it sounds like you were talking about the contrast color)