Neuroscience is interdisciplinary! To give you an idea, the neuroscience faculty at my institution (University of S. FL., RU/VH university) generally have Ph.D. in:
None of them are an M.D. so you have to ask where would medicine come in useful? Ph.D.'s do not generally interact with patients, perform medical procedures or do anything an MD is qualified to do (with respect to humans). Being said, you can have a dual MD/PhD where for example your MD is specialized health science and technology, and your PhD is specialized neuroscience. I think that for neuroscience research involving humans such as drug trials, behavioral neuroscience, etc. this is a preferred route. Some neuroscientists are then experts in computational studies as opposed to wet lab, where a data science background is helpful.
Some related publications by our faculty:
Hevers W, Hadley SH, Lüddens H and Amin J. Ketamine but not PCP selectively modulates cerebellar GABAA receptors containing a6 and d subunits J. Neuroscience. 28(20) : 5383-5393, 2008.
Segers LS, Nuding SC, Ott MM, Dean JB, Bolser DC, O'Connor R, Morris KF, Lindsey BG. Peripheral chemoreceptors tune inspiratory drive via tonic expiratory neuron hubs in the medullary ventral respiratory column network. Journal of Neurophysiology. 113: 352-368, 2015. http://www.ncbi.nlm.nih.gov/pubmed/25343784
At least with respect to reference one, the methods state results were obtained from rats/mice, from reference two they collected data from adult cats.
You can see that an MD or medical degree isn't necessarily required for a career in neuroscience. Some career postings I can see give preference to those who know some surgical procedures (not just for humans), but at the entry level I'm seeing 3yrs postdoc experience on top of the related PhD, to which you don't have to be embroiled in clinical decision-making and large amounts of blood (maybe on mice, etc.), publication record, etc.
For your intended program, you'll largely want to refer to your university of choice, mind you curriculum and requirements can largely vary by institution!