Recent analysis by researchers at the U.S. Census Bureau claims that by reconstructing the tabular data released from the 2010 Census, it is possible to reconstruct the original data and, using an accurate external data file with identity, reidentify 179 million respondents (approximately 58% of the population). This study shows that there are a practically infinite number of possible reconstructions, and each reconstruction leads to assigning a different identity to the respondents in the reconstructed data. The results reported by the Census Bureau researchers are based on just one of these infinite possible reconstructions and is easily refuted by an alternate reconstruction. Without definitive proof that the reconstruction is unique, or at the very least, that most reconstructions lead to the assignment of the same identity to the same respondent, claims of confirmed reidentification are highly suspect and easily refuted.