Can gravitational dynamics be obtained by diffeomorphism invariance of action?

It has recently been suggested that the gravitational dynamics could be obtained by requiring the action to be invariant under diffeomorphism transformations. We argue that the action constructed in a usual way is automatically diffeomorphism invariant in nature, which thus invalidates this alternative perspective to obtain gravitational dynamics. Especially, we also show what is wrong with the technical derivation of gravitational dynamics in the alternative approach.