The argument is not concerned with why people overestimate their odds—only that some people do. As such, whether or not the media is downplaying the odds of winning has no impact on the conclusion.

Even if other figures like politicians and celebrities receive media attention, the argument is unaffected. It could still be the case that at least someone out there sees news coverage of a winner and overestimates their odds as a result, so this isn’t necessary.

If this said, “If it were not for media attention, some people would not overestimate their chances of winning a jackpot,” it would be necessary. As it stands, however, it is too strong.

The author assumes that some people’s beliefs about their chances of winning the lottery can be affected by news reports of winners, and (D) addresses that assumption. If we negate it to say that nobody is led to overestimate their chances of winning because of the media, the argument falls apart.

This weakens the argument. We are looking for something that says people do overestimate their odds because of the media—not that some people don’t.