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The methodology in this case really isn't that unusual: it's not exactly the same as that used in for example political polling in the United States, but it's not far off - and, as the paper notes, it's exactly the same methodology as used to estimate deaths in other conflicts, including Kosovo and Darfur. If you believe those numbers, there's no reason not to believe the numbers in this paper (subject, of course, to the usual caveats about the statitical uncertainties involved).
The methodology is quite different from that used by Iraq Body Count, and IBC has been careful to point out that their totals are certainly underestimates of the total deaths resulting from the invasion. I think one of the most significant elements here is that the casualty trend lines (the changes in rates of casualties per time period, independent of the actual numbers) is very similar in this study, the IBC counts and DoD counts of casualties.
