I would think the contradiction is multiple contradictions, really. The anointed do not, to my knowledge, request anyone (ie. 'other sheep') to visit them when they are sick or in prison, nor do they (directly) ask for food or clothing. Jesus said nothing about support or obedience to 'the least of these my brothers'. He talked about acts of kindness. So the actual words written in Matthew 25 are discarded or rewritten to say, "To the extent that you obeyed the direction of the least of these my brothers, you obeyed me."
Also, if salvation depends on supporting these individuals, then faith in Jesus Christ has no actual role whatsoever. They didn't even say salvation depends on faith in Jesus Christ AND actively supporting his brothers. That might almost be forgivable. But with this framework, faith in Jesus Christ doesn't even matter all that much. The most basic tenet of Christianity has been shoved out of the picture.
I noticed that issue myself this weekend, though of course I wasn't at the meeting or anything. But it does make me realize that this is why people think JWs don't believe in Jesus. Because the insider doctrine puts "his anointed brothers" on equal footing with him and above everyone else. We're not brothers if some of us are joint-heirs with Christ and the majority of us are not.