I can see your point. However within the context of the "Church" the term "public" is meant as situations in which the setting is an LDS Church "public setting" (ie: Sacrament meeting, Sunday School, etc.) and secular "public settings" where the individual has been asked (or volunteered) to offer a prayer as an official representative of the LDS Church. As an individual baptized member of the LDS Church, a person is entitled (and encouraged) to offer prayers when situations arise with family and friends regardless of any formal Church restrictions.