It is generally believed that downlink cell-free networks perform best under centralized implementations where the local channel state information (CSI) acquired by the access-points (AP) is forwarded to one or more central processing units (CPU) for the computation of the joint precoders based on global CSI. However, mostly due to limited fronthaul capabilities, this procedure incurs some delay that may lead to partially outdated precoding decisions and hence performance degradation. In some scenarios, this may even lead to worse performance than distributed implementations where the precoders are locally computed by the APs based on partial yet timely local CSI. To address this issue, this study considers the problem of robust precoding design merging the benefits of timely local CSI and delayed global CSI. As main result, we provide a novel distributed precoding design based on the recently proposed team minimum mean-square error method. As a byproduct, we also obtain novel insights related to the AP-CPU functional split problem. Our main conclusion, corroborated by simulations, is that the opportunity of performing some local precoding computations at the APs should not be neglected, even in centralized implementations.