You are quite correct except that He was consciously involved. He asked: "who touched my garment"?.
Perhaps you are magnifying this episode into something much bigger than it actually was. This is one of the Gospels read during Lent in the Maronite Church. The message is actually quite simple. It is her faith that has healed her, not our Lord's garment. The woman believed that by touching the 'hem' of his garment, she would be healed. That touch transmitted her faith to our Lord who asked "who" had touched his garment. In a crowd of this size, many had touched his garment but this woman recognized Him as the Messiah and connected that recognition to the act of touching an article of clothing the He wore. She might just as easily have said "if I touch His hair", or "His hand", or "His toe" ... the point quite simply is that her faith in Him was transmitted by the touch and He responded to it, unlike all the others gathered around our Lord that day.
Jesus felt the power proceed from Him, and became consciously involved at that point, but by that time the woman was already healed.
It is her faith that has healed her, not our Lord's garment.
One does not exclude the other. It is true that others touched the garment without a similar effect, but it is also true that her faith found a focal point in the touching of the garment. It could have been anything else, yes.