<<Only the priest is the ordinary minister of the Eucharist (his hands are consecrated).>>
You are wrong on two counts:
1. The deacon and instituted acolyte are also ordinary ministers of the Eucharist.  The hands of deacons and acolytes are not anointed.
2. The anointing of the priest's hands signify his authority to preside at the Eucharistic celebration. It has nothing to do with distributing the Eucharist.