"if you're male then you're privileged"
without taking into account how a "privileged"
identity (such as maleness) may interact with
a "subordinate" identity (such as race), in
order to make one even less privileged
than holding two "subordinate" identities.
Like Mutua said, intuitively this doesn't
seem correct, but the studies bore it out
in the area of racial profiling and others.

To loosely quote her essay again:
"structures of race and gender {do} not simply
intersect but mutually and synergistically shape,
reinforce, and constitute one another,"
but people are so stuck on the rigid ideas of
the intersections that they aren't facing the
reality of the intersections.

And like you suggested, they end up downplaying
the oppression of groups based on the
assumption that they're supposed to be privileged
even when data doesn't bear it out.
It just becomes denial and disregard.

Thank god people are seeing through this mess tho.