Ok, so the real reason I posted this thread is because I want someone to tell me that you DON'T need that much medicine.
Well, I would be one who argures that a strong knowledge of IM is of immense benefit in neurology residency and practice. Stroke patients have a veritable plethora of cardiac issues, for instance. You may not always have cardiology or IM to come hold your hand for these problems, either. I suppose the best answer is it depends on the place you're training at and what you want to get out of the educational experience.
At my medical school, neurology was, ah, not strong. They would have an inpatient census of about 7 patients total, and would otherwise consult on everything. Acute strokes would often get managed by neurosurgery and internal medicine (in 2005). It was pretty cushy. On the plus side, there was a strong emphasis on outpatient general neurology. In retrospect, it was actually a good setup for residents seeking a true experience in ye olde traditional private practice general neurology.
In contrast, my residency was brutal. It was heavily focused on inpatient neurology, stroke, neurocritical care, and inpatient call. There would be 15-30 patients on the stroke service (admits, not consults), and 10-20 admits plus again as many consults on the general neurology side. Anything resembling an acute stroke was a stat call to neurology. Neurosurgey even managed to finagle us into admitting certain types of intracranial hemorrhages (which wound up being the *majority* of intracranial hemorrhages). Arrgh. Any stroke page (even courtesy of the EMT's en route to the ED) was the responsibility of neurology until proven otherwise, with precious little help from ED doctors in plenty of scenarios (to their credit, they were often busy with their own problems and not always just hanging out eating pizza their attendings had ordered). Resident clinics were full of non-insured, non-compliant, surly, patients who made up for lack of health care by having thick, psychiatric overtones emblazoned upon their neurologic disease.
Heaven help you if you wanted to learn some basic outpatient neuro. We had precious few months allotted for this, and they were jackhammered with an unending call routine, the fact that you could only take vacation during these self-same elective months, and the additional burden of the elective people having the responsibility of picking up basic science lecture/case report/journal club/grand rounds tasks.
Ah, the halcyon days of residency.
So you see the answer to your question can be quite different based on what type of program we're talking about here.
I was like you as a medical student. I hated internal medicine. But, during my internship I actually discovered that I enjoyed it about the month of October or so (much to my surprise). It turns out that you develop a knack for it quickly if you apply yourself and pay attention to the better attendings. Also, I fould a sense of humor goes far. Neurology often builds heavily upon internal medicine, and you may end up doing an awful lot of IM work in stroke and general neurology admissions if your residency is like mine was. In that case, I would suggest you get busy soaking up as much IM as you can. The senior neurology residents at your program can offer you advice about this.
The real world of academics or private practice? It'll be your choice. Pick a place that has minimal IM overlap in neurology (or the reverse) at your own discretion.