As a SUNY Binghamton student applying to medical school currently, I have found that I come across as a competitive applicant to many schools. I understand that Binghamton has a slight edge over Oswego in terms of reputation, but I doubt this slight decrease in reputation from SUNY school to SUNY school will affect all that much.
That being said... it will certainly be hard to gain admission to a top notch medical school. My GPA is very good, MCAT solid and EC's solid with mucho clinical experience and have not felt much love from the highly competitive schools.
Overall, Oswego should give you enough to get you into medical school AS long as you work your ass off. If you have acceptances to other colleges that have MUCH better reputation than Oswego, I would personally opt for them. Although I.S. tuition is a large perk. Any more questions just PM me.