Electroencephalography (EEG) plays a vital role in clinical and cognitive applications such as epilepsy diagnosis and emotion recognition. However, the low signal-to-noise ratio, inter-subject variability, and inherent non-stationarity of EEG signals present substantial modeling challenges. While recent Transformer-based models offer promising long-range modeling capabilities, their self-attention mechanism behaves as a low-pass filter, suppressing high-frequency neural patterns critical for decoding transient events. In this work, we provide the first formal analysis demonstrating this low-pass behavior in self-attention mechanisms when applied to EEG signals, revealing a fundamental limitation of deep attention-based EEG models. To address this, we propose SEBSFormer, a spectral-enhanced bi-Stream Transformer that jointly models temporal dependencies and spectral structures. SEBSFormer integrates three key modules: a spectral compensation module that restores high-frequency components via residual correction in the Fourier domain; a multi-scale temporal attention module for saliency-guided temporal compression; and a graph-guided dynamic fusion module for adaptive spatial aggregation across electrodes. Extensive experiments on three benchmark datasets—TUAB, TUEV, and SEED—demonstrate that SEBSFormer consistently outperforms existing state-of-the-art models across both clinical and affective tasks. Our findings establish a new paradigm for frequency-aware EEG modeling.