I don't know about this. These days, I've seen and met many women who have numerous male friends. Sure, ultra-conservative and religious women don't, but lots of women aren't conservative any more.
To put it bluntly, the colloquial prevalence of "thinking with your [genitals]" certainly indicates that people's higher social brain function tends to be clouded more often (reverting to base instinct) when sex is involved.
(Obviously, good relationships are based on friendship as well, but by definition the relationships in this study were not successful ones.)
This premise and your thoughts on polygamy can coexist with my suggestion about women being selective. If you can have only a handful of pregnancies in your lifetime each of them carrying the very real risk of death for both yourself and the baby, as well as the burden of taking care of any children that survive, then you really need to make sure that your shots count and you're choosing the best mates from the tribe. Men don't have the same burden of pregnancy and childcare - additional partners only increase their chances of passing along their genes, so as a result they become far less selective.