I've read a lot of things that seemed so outlandish, that were outlandishly false, that my brain had such a hard time comprehending it that I would stumble along and would have to reread passages over again. My brain would stumble a lot like DeNiro in this video. When I read stuff that I know to be false, as I'm reading my subconscious brain tries to hijack the conscious part and force me to quit because it knows propaganda when it sees it, and it then becomes extremely difficult for me to focus and finish the task.

So, my theory with this, is that DeNiro most likely doesn't believe what he's reading. His brain is immediately recognizing outlandish propaganda and has lost its focus and is trying to leave the situation, so he's stumbling across the sentences because his conscious brain is saying that he has to finish since he's now in the spotlight and leaving without finishing means he loses credibility, and possibly even loses whatever money they were paying him. He's literally battling himself to finish because this could potentially ruin him if he were to admit the truth and quit.