First, it is most certainly not bread and wine, the correct terminology would be Body and Blood of Christ, Holy Communion, Host and Cup, or Eucharist.
That said, the actions of the person was correct, although the explanation a bit off. Intinction, the dipping of the Host in the Cup, is allowed in the Catholic Church, but it MUST be done by the priest or deacon, not by a lay person. We RECEIVE Holy Communion, never take, and dipping would essentially be taking. To receive by intinction, the priest would take the Host, dip it in the Cup, say “The Body and Blood of Christ” and place it on your tongue.
Also a note, not allowing the Body and Blood of Christ to mix would make no sense as the priest does this at ever Mass. He takes a small piece of the Host and places it into the main Chalice while praying quietly “May this mingling of the body and blood of our Lord Jesus Christ bring eternal life to us who receive it.”