You may have seen the video, but I think your interpretations were 100% incorrect. Lay people are “trained” to be Extraordinary Ministers of Holy Communion and are allowed to distribute the host to the faithful (I am one). So there is definitely NO teaching / rule that states a lay person cannot touch the host.
As it stands now, that is the law of the Church, but since St. Thomas Aquinas is a high authority in the Latin rite, he taught that only those with consecrated hands should touch the Blessed Sacrament.