This seems a bit too pat to me, as though men were cardboard cutouts only able to be one thing. I propose an alternative interpretation: that when fertile a woman wants a different role from her man--that he be more "take-charge" when her body wants to get pregnant. This seems to explain the evidence about as well, without the problem their interpretation has that the risks of infidelity are at least as high to the children as the purported benefits. ("Not my kid, why should I support it--or you, either?")
The greater the difference between the father and the husband, the more likely the child is to be recognized as not the husbands; but the smaller the difference the smaller the presumed differential "fitness" of the child--so why bother?