Answer: The exerspy passes all required standards for medical devices of this type regarding electro-magnetic radiation. The standards it passes are equal to or stricter than those for consumer devices.
The armband does have a radio which communicates with the display. The range is specified as 3 meters (about 10 feet, line of sight, no walls, windows, people in betwee,n etc). The radio only broadcasts if requested to by a display or other BodyMedia accessory. If you do not use the display, then the radio will only turn on when you press the armband button which prompts the radio to listen for 1 minute.
The user guide lists standards tested and passed. Download the exerspy
armband user guide here.