Yes, because in the sort of patriarchal dominance hierarchy I've been describing white women are higher up the pyramid than black men in some respects. But privilege is intersectional. You can both be privileged in one area and oppressed in another. Black men were granted the right to vote a full 50 years before white women. That says a lot right there.
I'm well aware of how white feminism has made the movement all about it's own empowerment to the detriment of our black sisters. I've written about it often. The only issue isn't between men and women (although it is a significant one), it's about all of the stratification inherent in a patriarchal dominance hierarchy.
White women have a fair amount of institutional power relative to everyone else - other than white men. This country was established for the interests of white men and a mere 60 years ago we still had laws that codified that. Those beliefs don't disappear just because the laws have changed. If an alien race viewed our media, they'd think that white men make up 70% of the population rather than the 30% which is actual.
It's an incredibly androcentric culture where men still hold the bulk of power and prestige. That means the power dynamics are still highly skewed in favor of men, even black men in many cases.
When school aged boys are asked what it takes to be a man, being dominant over girls/women is one of the four main things that they cite. Even young boys know this and are conscious enough about it to be able to verbalize it. This is still very much the fabric of our society. Class stratification, race stratification - those things are certainly an important part of the mix, but 50 years ago a woman couldn't get a home or business loan in her own name. She had to have a man co-sign. She couldn't get a credit card in her own name. She couldn't go to an Ivy League school (except Cornell, which always accepted women). She could be fired for being pregnant or struck from a jury simply for being female. These are fundamental elements of our culture that we have come a long way on but not nearly begun to transcend.
White men still hold the bulk of power in this society. Ergo, they are more directly responsible for it's ills in part because so many of them are still clinging tooth and nail to the right to preserve that place in the hierarchy at the expense of everyone else.