Recently, several experimental works have appeared in the literature where induced magnetism in single- and few-layer graphene (SL-gr and FL-gr) interfaced with layered van der Waals materials was investigated via the application of the anomalous Hall effect (AHE). In most of these works, it is suggested that the observation of the AHE in such systems can be explained by a magnetic exchange interaction appearing at the interface between graphene and the underlying magnetic insulator. Considering the recently studied FL-graphene/bulk-CuCrP2S6 system as an example, our careful and rigorous analysis of recent experimental and theoretical data presented in the literature shows that the claimed observation of the AHE and magnetic proximity effect in this system is not supported. Moreover, the theoretically calculated electronic structures of the studied system contain serious errors and flaws that cannot be considered as an accurate description of such an interface and cannot be taken as solid support for the proposed proximity effect.