Chip Timing (RFID Tags), have a variety of antennas utilized in reading the tags. These antennas have a field that will vary in size based on the antenna type, brand of technology and the placement of the antennas. The chips can read anywhere within the field.
Place in cross country is determined by the "torso" crossing the plane of the finish line. The finish line, similar to track and field, is 5 cm wide to 30 cm wide, but the front edge of the finish line is where the course is measured.
Even though chip timing is allowed for official results for cross country, there needs to be an accurate form of backup to verify placement of runners, specifically at critical competitions (but it should be used at all). Go to the link below, an article on MileSplit discusses where the runners finished in different order based on rules and the chip timing data. Ask any coach and most athletes, they will tell you that place is determined by the torso and not the foot or an arm.
The article below discusses critical team placement (3rd and 4th) based on the chip results to qualify to the next level of competition.