I doubt it is true, at least in Russian history a typical peasant had a wife and children. Not being married was considered bad and there were arranged marriages. Also poor men probably had a low chance of "getting laid" as girls were interested only in lifetime long relationship.
I even tried to verify this by looking through old registries available online (where marriages and births were recorded), some of which are digitized and OCR'd by Yandex, but it seems that they do not have a list of unmarried people. Although the birth records typically mention whether a child is "legally born" (within a marriage) or not.
GP is correct. Human history spans hundreds of thousands of years. You are talking about the most recent ca. 5000 years of enforced monogamy through the social/cultural institution of marriage, but this era has come to an end and we are reverting to the natural state of affairs (polygyny) again.
I even tried to verify this by looking through old registries available online (where marriages and births were recorded), some of which are digitized and OCR'd by Yandex, but it seems that they do not have a list of unmarried people. Although the birth records typically mention whether a child is "legally born" (within a marriage) or not.