I'm not saying that the majority is not Shiite or that the government isn't Sunni (though it's more secular than that would lead you to believe), but that extracting the Kurdish and Ma'dan Shiite pupulations leaves you with a majority of Sunnis. The issue is whether or not the 80% Shiite population is concentrated in the north and south as Kurds and Ma'dan. This map shows that the population is mostly distributed that way, but it doesn't show density.

Edit: This article claims that The Sunni to Shiite ratio is much closer than Roger posited, at 52:42, which means that leaving out the Kurds, who are surely nearly 100% Shiite, at 19%, acording to that article, the Sunni claim a majority, and that's not touching the Ma'dan.

Other articles claim other ratios, which could easily make my argument inaccurate. That was just the first on Google.