How much flexibility does your unit command have in discharge proceedings?

I joined the Army last July and early this year had a medical issue come up that is possibly related to a preexisting condition that I did not tell the Army about when I joined. According to Army regs this condition should have barred me from enlistment and will not allow me to stay in. Obviously, technically I know should be getting a fraudulent enlistment discharge, but my company commander, first sergeant) have told me that they will just get me a general discharge, if I have to be discharged (they said they would push for me to be able to reclass). Do they actually have that power/flexibility to prevent a servicemember who should be getting a fradulent enlistment discharge downgraded to a general or bypass discharge altogether and let a servicemember reclass? I do know we had guys in my unit fail drug test and they just got general discharges if that information helps.