I provided a pair of quotes above. Do a word study on “demons” and “healing” in the New Testament and you will find more instances when healings are mentioned distinctly from exorcisms.
While that may be true in many cases among ignorant and superstitious people, it does not preclude the fact that there are actual demons and that they do, in fact, occasionally possess people and need to be exorcised. If the New Testament makes the distinction, it should be taken at face value.
I can’t guess the motivations of whoever put the notes for your study Bible together, but much thinking like this about miracles and demonic activities comes out of mind-set that, because people that came before us (including those who wrote the Bible) were less technologically advanced than us, they must have been stupider and unable in any circumstance to differentiate physical illness (which may include mental illness–the Bible doesn’t make any distinction) from demonic possession. If the notes in your Bible say, “She probably suffered a serious mental or physical illness…” but don’t give any evidence to back their assertion, they’re just making an unsubstantiated supposition.
I recommend the book below if you would like more reliable information about possesion and exorcisms.
Interview With and Exorcist, by Fr. Jose Fortea