This is a nonsense statement. A dowry is provided by the bride's family and a girl with a substantial dowry would have her pick of spouses, not be married off to an old man. Depending on the culture, the dowry may indeed go to the couple and be the bride's personal property and not enrich the groom's family.
It is cultures where brides must be purchased that young girls end up with old men. This is frequently seen in polygynous societies because older, wealthier men with multiple wives create a scarcity of women in the marriage market and drive up the average cost of a bride.
One of the most vicious examples of dowry today is in India, with the practice of bride burning. Because women sold by dowry become members of her husband’s family, and there is a strong prejudice against remarriage for women, but not men, as soon as the groom’s family gets the dowry, one of them pours gasoline on the bride and sets her on fire.
Then their son can get remarried, and get another dowry.
http://en.wikipedia.org/wiki/Bride_burning