This paper develops a robust physics-informed state estimation method for the distribution network with inaccurate topology information. An aggregated k-nearest neighbor graph is first derived as the feature graph according to the inaccurate topology and measurement features. Then, graph propagation and aggregation are performed by an adaptive multi-channel graph attention model on both the feature graph and the graph constructed based on the inaccurate given topology. To fuse the different graph embeddings, an attention module is further employed to adaptively assign importance weights for them. This allows the proposed method to achieve robustness against anomalous measurements even when the given topology information is inaccurate. Comparative results with state-of-the-art distribution system state estimation methods demonstrate the accuracy and robustness of the proposed method.