I think you’ve hit on it - at least to some extent. In my experience God works within the framework of one’s understanding (i.e. He meets them where they are.) Those in other countries have very real, palpable experiences with demonic powers. They truly NEED deliverance from them. Not every illness or physical ailment is demonic. God has said “It is appointed unto man once to die and after that the judgment.” Death is not optional. Barring His return first, all flesh will die. While physical healing is wonderful in and of itself (and miraculous healing DOES occur, but most often the physician or medicine gets the credit), the point in this story is that this girl was rid of a demon and came to Christ. It is eternal redemption which concerns God more. She could not come to Christ AND have a demon within her. One precludes the other.
Sadly,,I think the real reason,is that people over there believe the Bible,,Take it at its word so to speak.While here we think its all just a nice story,not truly real.I see too many pastors saying its just a story,or only for those times,not for today.That it could be explained away by modern thinking,medicine,or science.We make far too many excuses for not believing.