I hate to use "n=1" as an argument for that, but that really is an isolated opinion. There are plenty of ophthalmologists at the university I attend that care about a great deal of organs besides the eye, and frequently have made systemic diagnoses. There are two areas where this can pop up that I can think of off the top of my head:
1) consults -- to provide a proper consult for another service (e.g., Internal Med), one would have to know their structure, protocol, and what's important/feasible in a way that's not possible if one only has knowledge of the eye. All physicians have rotated through an IM clerkship, and (should) have a knowledge of how to provide an effective consult -- nothing is more frustrating than a consult that shows clearly no knowledge of the patient's other problems.
2) operative risk -- both in terms of anesthesia, and for a feel for when operation is worthwhile, vs when a patient's comorbidities make it silly to take his cataracts out.
It's a lot of small things, but small things done right = good patient care. Not that ODs can't do it necessarily, but the formal training is not there.