Wireless communications is often subject to channel fading. Various statistical models have been proposed to capture the inherent randomness in fading, and conventional model-based receiver designs rely on accurate knowledge of this underlying distribution, which, in practice, may be complex and intractable. In this work, we propose a neural network-based symbol detection technique for downlink fading channels, which is based on the maximum a-posteriori probability (MAP) detector. To enable training on a diverse ensemble of fading realizations, we propose a federated training scheme, in which multiple users collaborate to jointly learn a universal data-driven detector, hence the name FedRec. The performance of the resulting receiver is shown to approach the MAP performance in diverse channel conditions without requiring knowledge of the fading statistics, while inducing a substantially reduced communication overhead in its training procedure compared to centralized training.