Believing the terrorist is mentally ill is less frightening than believing that a sane person could commit such indiscriminate violence against innocent strangers. There's a madness present, clinical or otherwise.
Truth is, we often do not know mass killers' mental health status or their motive because they are killed or kill themselves before they can be captured. Examining their lives retrospectively for signs of instability is speculative and tenuous. 
Your concern to protect the mentally ill from being stigmatized as dangerous is understandable, doctor.