In biblical times, women did have the right to claim the marital protection due to them. For example, in Deuteronomy 25:7–10, the remedy is explained for when a man did not want to do his duty and marry a widowed kinswoman. In the story of Ruth, Naomi merely suggests an expedient way of asking Boaz to stake his claim. He is not the closest kin, but he is the one whom Naomi knows that Ruth prefers (cf. Ru 3:1).
In a time when people rarely married for romantic love alone, Naomi wanted to help Ruth make a match that was to her preference rather than the one that was required by the law. Boaz still had to agree to the match and both Ruth and Boaz had to hope that the kinsman with prior claim would renounce it (cf. 3:13). Interestingly enough, in chapter 4 Boaz—of his own initiative—maneuvers the kinsman to renounce his claim by pointing out the duties the kinsman will have to take on in addition to marrying Ruth (4:5).