We present a new theoretical method to treat atom-rigid bender inelastic collisions at the Close Coupling (RB-CC) level in the space fixed frame. The coupling between rotation and bending is treated exactly within the rigid bender approximation and we obtain the cross section for the rotational transition between levels belonging to different bending levels. The results of this approach are compared with those obtained when using the rigid bender averaged approximation (RBAA) introduced in our previous work dedicated to this system. We discuss the validity of this approximation and of the previous studies based on rigid linear HCN. We find that l-type transitions cross sections have to be calculated at the RB-CC level for the He-HCN collision while pure rotational transitions cross sections may be calculated accurately at the RBAA level.