As generative artificial intelligence evolves, autonomous agent networks present a powerful paradigm for interactive covert communication. However, because agents dynamically update internal memories via environmental interactions, existing methods face a critical structural vulnerability: cognitive asymmetry. Conventional approaches demand strict cognitive symmetry, requiring identical sequence prefixes between the encoder and decoder. In dynamic deployments, inevitable prefix discrepancies destroy synchronization, inducing severe channel degradation. To address this core challenge of cognitive asymmetry, we propose the Asymmetric Collaborative Framework (ACF), which structurally decouples covert communication from semantic reasoning via orthogonal statistical and cognitive layers. By deploying a prefix-independent decoding paradigm governed by a shared steganographic configuration, ACF eliminates the reliance on cognitive symmetry. Evaluations on realistic memory-augmented workflows demonstrate that under severe cognitive asymmetry, symmetric baselines suffer severe channel degradation, whereas ACF uniquely excels across both semantic fidelity and covert communication. It maintains computational indistinguishability, enabling reliable secret extraction with provable error bounds, and providing robust Effective Information Capacity guarantees for modern agent networks.