True, to an extent. Each has an interest in faithfulness, but of a different type.
A woman’s emotionless one-night stand can result in pregnancy and is thus against her male partner’s interest. A woman might tend to find it less threatening if her male partner had a one-night stand.
A man’s emotional affair is threatening to his female partner, because it means her partner might leave. A man might find his partner’s emotional affair less threatening.
There are also reproductive strategies for both sexes that rely on being unfaithful. There is biological evidence that humans are not strictly monogomous. I’ve written a little about it here: