We can gauge the Syrian government's legitimacy by the simple fact of the internally displaced Syrian citizens going back to Syrian cities after the army has removed FSA and allied groups.
Among the cities seeing the returns are Hama and Homs. These people trust the government to guard them.
Add to that what
@mohammad45 said.
The Syria conflict, like the Libya conflict, is not a civil war. It is a international war intended to convert Syria into NATO ally country by removing the Ba'athist government and replacing it with a NATO friendly one.