No fly/military restricted zones in Indonesia


When volcanic eruptions and ash clouds occur in the vicinity of Bali in Indonesia, local airlines including Garuda and Air Asia cancel their flights a lot less than international airlines. I have heard various explanations including that the local airlines have access to flight routes that other airlines don’t, and that they have access to military no fly zones that other airlines don’t.
Are there military or special no fly zones in that area? Are there special rights to additional routes from some local aircraft?