The only people testable in a surname DNA test would be males. The DNA used in this test is YDNA. All other DNA is disregarded. Every male has only one Y chromosome. Females have none. The part of the Y chromosome tested is directly passed from father to son. There is never any maternal influence. Extremely few inherited traits are in this Y DNA.
Therefore, having two descents from earlier Fitts would not show up in the test.