I can't say if this qualifies as scientific, but perhaps a wider grip forces the elbows further apart and thus further back? Does having the elbows out rather than in work one better?
I can't really figure it out, to be honest. This is flexion vs. abduction. What gets confusing is since our scapulae rotate upwards, it makes it harder to visualize the line of pull with the delts due to that rotation.
When elbows are in, and in front of us, and we press up, that's flexion. When the elbows are out, to our left and right, forming a line midway through the press, that's abduction.
Of course, I doubt anyone does these perfectly and likely when we press we are somewhere in between these two extremes. But a close grip makes it hard to move the elbows out, just as a wide grip makes it hard to move it in.
Due to the influence on elbow width (much like with bench pressing or rowing) that could explain different muscular emphasis.
The only thing is... when our arms are externally rotated, I thought the anterior deltoid provided the adduction. Or I guess we might call it abduction, but if you think of how it adducts in the transverse plane when neutral (like in a bench) if we externally rotate, we're pointing the anterior deltoid upwards so it's still performing that function of drawing towards the midline (overhead in this case) even if in our circumductory fashion we call it abduction.
Conversely, I wonder how the medial deltoid works during presses like this. What we know is that internal rotation shifts the work back and external rotation shifts the work forward, we see this when we do a rear delt row, if the elbows point back it's more rear delt and if you externally rotate, it allows the medial delt to work.
When we're in neutral position, the anterior deltoid works as our shoulder flexor, like when we do a forward dumbbell raise. So, what happens if we externally rotate (elbows down hands up) into the overhead pressing position? Could the medial delt become a shoulder flexor?