Actually, the opposite is true. There's no single explanation for it, but women tend to survive in much higher numbers during times of severe famine or catastrophe. It's likely a combination of several factors: Women have slower metabolisms and higher bodyfat, and they tend to form more close knit groups. Men tend to take on more physical labor, they tend to waste more energy, and are more likely to end up as social outcasts.
I think a collapse of civilization will be hard on women yes. I'm not misogynistic and am an advocate of equal rights for all sexes but there are hard realizations about the sort of behavior we would exhibit in the wrong sort of circumstances.
Id suggest anyone not affiliated to a larger group would be in danger. I agree an outcast solo man might fare slightly better on their own, but in a dynamic enviro with other people a woman might fare slightly better.
This is how a lot of men expect things to go even within society. Sexual assault is ostensibly illegal but in practice does not always result in harsh penalties.