This is an interesting point. The verses cited in Matthew don't seem to support the Society's explanation either. See Matt. 26:25-35:
25 By way of reply Judas, who was about to betray him, said: “It is not I, is it, Rabbi?” He said to him: “You yourself said [it].”
26 As they continued eating, Jesus took a loaf and, after saying a blessing, he broke it and, giving it to the disciples, he said: “T AKE , eat. This means my body.” 27 Also, he took a cup and, having given thanks, he gave it to them, saying: “Drink out of it, all of YOU ; 28 for this means my ‘blood of the covenant,’ which is to be poured out in behalf of many for forgiveness of sins. 29 But I tell YOU , I will by no means drink henceforth any of this product of the vine until that day when I drink it new with YOU in the kingdom of my Father.” 30 Finally, after singing praises, they went out to the Mount of Olives.
31 Then Jesus said to them: “All of YOU will be stumbled in connection with me on this night, for it is written, ‘I will strike the shepherd, and the sheep of the flock will be scattered about.’ 32 But after I have been raised up, I will go ahead of YOU into Gal´i·lee.” 33 But Peter, in answer, said to him: “Although all the others are stumbled in connection with you, never will I be stumbled!” 34 Jesus said to him: “Truly I say to you, On this night, before a cock crows, you will disown me three times.” 35 Peter said to him: “Even if I should have to die with you, I will by no means disown you.” All the other disciples also said the same thing.
Of course, there is a passage that the Society uses to support its teaching that Judas left the last supper before the disciples ate the bread and drank the wine: John 13:26-30:
26 Therefore Jesus answered: “It is that one to whom I shall give the morsel that I dip.” And so, having dipped the morsel, he took and gave it to Judas, the son of Simon Is·car´i·ot. 27 And after the morsel then Satan entered into the latter. Jesus, therefore, said to him: “What you are doing get done more quickly.” 28 However, none of those reclining at the table knew for what purpose he said this to him. 29 Some, in fact, were imagining, since Judas was holding the money box, that Jesus was telling him: “Buy what things we need for the festival,” or that he should give something to the poor. 30 Therefore, after he received the morsel, he went out immediately. And it was night.
My understanding is that the "morsel" described in verses 26 and 30 is not the communion bread of which J.C. and the apostles partook. I always understood that that the morsel was just part of the regular meal.
Anyway, it looks like Luke and John are in conflict (or more bluntly, they are contradictory). Hence the Society explains it away by saying that Luke's account is not in chronological order. Now what sense does that make?