We demonstrate analytically that the contribution of cooperation in improving the accuracy of distributed network localization has a fundamentally structural nature, rather then statistical as widely believed. To this end we first introduce a new approach to build Fisher Information Matrices (FIMs), in which the individual contribution of each cooperative pair of nodes is captured explicitly by a corresponding information vector. The approach offers new insight onto the structure of FIMs, enabling us to easily account for both anchor and node location uncertainties in assessing lower bounds on localization errors. Using this construction it is surprisingly found that in the presence of node location uncertainty and regardless of ranging error variances or network size, the Fisher information matrix (FIM) terms corresponding to the information added by node-to-node cooperation nearly vanish. In other words, the analysis reveals that the key contribution of cooperation in network localization is not to add statistical node-to-node information (in the Fisher sense), but rather to provide a structure over which information is better exploited.