Consider a generalized multiterminal source coding system, where $\begin{pmatrix} \ell\\ m \end{pmatrix}$ encoders, each observing a distinct size-m subset of $\ell(\ell\geq 2)$ zero-mean unit-variance symmetrically correlated Gaussian sources with correlation coefficient $\rho$ , compress their observations in such a way that a joint decoder can reconstruct the sources within a prescribed mean squared error distortion based on the compressed data. The optimal rate-distortion performance of this system was previously known only for the two extreme cases $m=\ell$ (the centralized case) and m = 1 (the distributed case), and except when $\rho=0$ , the centralized system can achieve strictly lower compression rates than the distributed system under all non-trivial distortion constraints. Somewhat surprisingly, it is established in the present paper that the optimal rate-distortion performance of the aforedescribed generalized multiterminal source coding system with $m\geq 2$ coincides with that of the centralized system for all distortions when $\rho\leq 0$ and for distortions below an explicit positive threshold (depending on m) when $\rho > 0$ .