I do not think that it is simply the addition of the Holy Body to the wine which consecrates it but, at the risk of sounding scholastic, the intention and action of the priest. The Syrians who invented the service used a prayer or at the least required the priest to meditate silently about what he was doing. The Byzantine Presantified Liturgy also has the remnants of this.
After the Fraction at a regular Liturgy the deacon tells the priest: "Master fill the Holy Chalice". At which the priest takes the IC portion of the Holy Lamb, makes the Sign of the Cross over the chalice with it, and places it in the chalice saying "The fullness of the Holy Spirit". In the Liturgy of the Presanctified the deacon says instead: "Master bless the chalice". The priest however does the same as at normal Liturgy.
I see this as a minor Epiclesis and clearly the priest's blessing and power is invoked.
In further support of the lay persons inability to accomplish this act, we know that in St. Basil's day the laity took home and preserved the Holy Body for daily Communion. We aslo know intinction was not yet practiced. They did not take home the Holy Blood and it is never mentioned that the laity were allowed to place the Holy Body into wine at home but that they broke their fast in the morning with it, eating it alone before anything else. Once intinction became the norm, reservation of the Holy Gifts for hermits was done by intincting the Holy Body with the Holy Blood. If a layperson could perform the act there would be no need to intinct the Holy Body with the Holy Blood. However this intinction was not done for Presanctified because of the wine that woud be consecrated at it. (The intinction is done now by most if not all Orthodox priests and some Catholic priests.)
Fr. Deacon Lance