Medula oblongata controls the involuntary actions & the reflex actions are also involuntary actions- so why the middle oblongata does not control reflex action?

Medula oblongata is responsible for controlling the involuntary actions like blood pressure, vomiting etc. It doesn't control reflex action as it is a part of the brain. Reflex action is a type of action that occurs in the fastest way possible. The reflex action is thus controlled by spinal chord, which belongs to the Central Nervous System (CNS) for a faster decison making process. The brain just gets informed about the incident that happened at the end. If medula oblongata controls this process, then indirectly the brain would control it which would lead to more decision making time and thus might cause damage.