JOEL - It is true that for a long time only Melchizedek Priesthood holders were the only ones who gave the prayers in Sacrament meetings. The likely reason for this was because the Sacrament is a priesthood ordinance, and therefore all prayers given in the Sacrament meeting were restricted to priesthood holders.
During the 1970s women's lib was getting into full swing and a few women were complaining that they were not being allowed to participate as much as they should in church meetings and leadership positions. The Church leaders did not change any doctrine or official policies because of this, but I think they did realize that there was no scriptural reason for why women could not pray in Sacrament meeting. It was mostly out of tradition that only priesthood holders would give the prayers. It was then that they decided to encourage Bishops to call on both men and women to pray. In 1978 the following announcement was made:

“The First Presidency and Council of the Twelve have determined that there is no scriptural prohibition against sisters offering prayers in sacrament meetings. It was therefore decided that it is permissible for sisters to offer prayers in any meetings they attend, including sacrament meetings, Sunday School meetings, and stake conferences. Relief Society visiting teachers may offer prayers in homes that they enter in fulfilling visiting teaching assignments.”
(Marvin K. Gardner, “News of the Church,” Ensign, Nov. 1978, 100)

Who won the bet; and what's my percentage? :-)