The lats do not assist in scapular depression because it slips by the inferior angle of the scapula. While the lats are not a prime mover, scapular downward rotation and depression are assisted by the lats by the adductive and extensor forces at the GH joint.
This is not the case: while some people may not have significant fiber attachment at the inferior angle due to genetic variation, it's widely accepted that the lat does in fact attach either directly or through fascial attachment to the inferior angle, therefore being capable of causing motion at the scapula directly.
From
Wheeless' Textbook of Orthopaedics (one of many possible sources of this information):
Latissimus Dorsi
- origin: broad aponeurosis that originates on the spinous processes
of the lower 6 thoracic and all lumbar vertebrae; posterior crest
of ilium, posterior surface of sacrum, lower 3 or 4 ribs,
and an
attachment of the tip of the scapula;
- insertion: flat tendon that twists upon itself to insert into the
intertubercular groove of the humerus, just anterior to and
parallel with the tendon of pectoralis major;
- nerve supply: thoracodorsal from brachial plexus, C6, C7, C8;
- action: extends, adducts and medially rotates the humerus at the
shoulder;
draws the inferior angle of the scapula inferior and
medial; (draws shoulder downward and backward);
- synergists: rhomboids, pectoralis major, teres major;