Consider this - according to Luke's gospel Jesus presented the symbols of his body and blood to none other than Judas. Yes the very guy that was getting ready to betray him.
Maybe someone will get this thought better than I got it. (I forget so much so fast after leaving the JW's) JW's teach that Judas left the room before the covenant part of their meal. To fudge the point without highlighting it during the memorial talk, they say that it was a covenant Jesus made with his "faithful apostles."
That and some scripture that allows one to be led to believe such a statement bolsters the claim that only the "anointed" partake.