Another way to come at this problem is to ask this question:
If the 1913 image is not the 12th green, then which green is it?
The 12th green was quite famous and oft discussed because of the huge mounds on the green. I've never read any discussion of any other hole at Garden City with similar mounds on the green.
Patrick says there were other greens with mounds nearby, but these mounds aren't nearby, they are right on the green or very closely flanking it, and think about how small the green would have to have been for these mounds to be flanking mounds! I am unaware of any other early green at GCGC which fit the description, and I believe that such an oddity would have been discussed. (Like the 12 green was discussed.)
Patrick suggests the green on the first hole, which a well known (and copied) hole. I've never read any description of such mounds at the 1st green. Also, look at the 1913 image of the bunker abutting the first green, on the previous page. No mounds are visible, yet if this was the same bunkern, we ought to at least see part of the small front right mound which is visible in the old aerial in the ground level image.
Also, notice the mowing lines up into the mounds, particularly the large right mound. The grass is visibly cut short right up into the mound, suggesting it was on the green or at least abutting the green.
I've cropped the 1913 image so it fits on the page, and highlighted where I see the borders of the mounds. To me they are a pretty good match of the old aerial.
If this isn't the 12th green, then which green is it?
While I can see why you guys have doubts, the photo fits much better with the 12th green than anything else on the course (or anywhere else for that matter.)