Graph deep learning models, a class of AI-driven approaches employing a message aggregation mechanism, have gained popularity for analyzing the functional brain connectome in neuroimaging. However, their actual effectiveness remains unclear. In this study, we re-examine graph deep learning versus classical machine learning models based on four large-scale neuroimaging studies. Surprisingly, we find that the message aggregation mechanism, a hallmark of graph deep learning models, does not help with predictive performance as typically assumed, but rather consistently degrades it. To address this issue, we propose a hybrid model combining a linear model with a graph attention network through dual pathways, achieving robust predictions and enhanced interpretability by revealing both localized and global neural connectivity patterns. Our findings urge caution in adopting complex deep learning models for functional brain connectome analysis, emphasizing the need for rigorous experimental designs to establish tangible performance gains and perhaps more importantly, to pursue improvements in model interpretability.