I think they get us to belive it via sleigh of hand with the following Bible text from Luke 22 at the last supper.
Jesus has demonstrated the New Covenant, then some time later, an argument breaks out amongst the Diciples about who would be the greatest, after Jesus puts them right he "confers" on them places in his Kingdom to rule as Kings with him, because they stuck with him in his trails.
Nowhere does it say that the New Covernant is for anyone to rule as Kings, it says its for forgiveness of sins due to Jesus sacrifice, whereas the Old Covernant was salvation by works.
The bit about Kings that the JWs use, though it appears in the next paragraph, its clear its not related.
19 And he took bread, gave thanks and broke it, and gave it to them, saying, “This is my body given for you; do this in remembrance of me.”
20 In the same way, after the supper he took the cup, saying, “This cup is the new covenant in my blood, which is poured out for you. [a] 21 But the hand of him who is going to betray me is with mine on the table. 22 The Son of Man will go as it has been decreed. But woe to that man who betrays him!” 23 They began to question among themselves which of them it might be who would do this.
24 A dispute also arose among them as to which of them was considered to be greatest. 25 Jesus said to them, “The kings of the Gentiles lord it over them; and those who exercise authority over them call themselves Benefactors. 26 But you are not to be like that. Instead, the greatest among you should be like the youngest, and the one who rules like the one who serves. 27 For who is greater, the one who is at the table or the one who serves? Is it not the one who is at the table? But I am among you as one who serves. 28 You are those who have stood by me in my trials. 29 And I confer on you a kingdom, just as my Father conferred one on me, 30 so that you may eat and drink at my table in my kingdom and sit on thrones, judging the twelve tribes of Israel.
Interesting that it is only Lukes Gosple that makes any mention of the ruling as kings dispute and promise, Matthew and Mark mention the eating of the Symbals of the New Covernant being for forgiveness of sins and as a rememberence of him, but nothing about the ruling as kings.
Its just another case were the JWs match two unrelated Biblical passages in order to get folk to belive in theri doctrines of men.