A flesh-eating virus is a misnomer.
They're not responsive to stimulus, and they also do not carry out respiration. They do not grow through cell division; they need to hijack a host cell for its duplication machinery to start reproduction of their own genetic blueprints. Furthermore, there is no stopping a virus, like a chemical reaction, once started it must run its course, prevention is key. Although, in some scientific communities debate continues whether to consider a virus living or an organic structure; viruses do not have a metabolism so they will never eat.
The virus Ebola hemorrhagic fever interferes with platelets cells and the cells lining the interior of blood vessels, and in the fatal stages the damage can cause a person's body to leak blood from their eyes, ears, and anus but the virus will never feast on the sludge that once was a body.
Most likely, the Ebola virus lead to the inaccurate nomenclature we have today.