From Bradford White website pdf:

"Place the draft diverter over the flue opening at the top of the water heater by
inserting the tips of the draft diverter legs into the four (4) holes provided in the
water heater top. On some models, line up the holes in the draft diverter legs
with the holes provided on top of the water heater. Secure the draft diverter to the water heater with sheet metal screws."

Not the clearest writing, but it appears they are saying you only have to use screws on those models that have holes for screws.