Angular replace array in $scope and $apply doesn't work

I have a fairly large Angular app with 15 directives and 5 services. The problem I'm having is related to updating the local scope from within a service. And with updating I mean replacing the array the scope is pointing at to another array.

The process is the following after I click an element:

clickDirective () {
    restrict: 'A'.
    link: function (scope, element, attrs) {
        if ($rootScope.hasCertainValue) {
            FirstService.handle(scope, valueX)
        }
    }
}

/* Calls FirstService.handle */

FirstService () {
    handle (scope, valueX) {
        if (certainCriteriaMet) {
            SecondService.handle(scope, valueX)
        }
    }
}

/* Calls SecondService.handle */

SecondService () {
    handle (scope, valueX) {
        /* This is the funny part*/
        console.log(scope.value) // let's assume prints: ['a']
        // Option a)
        scope.value = ['a', 'b'] // this is what I want to do
        // Option b)
        scope.value.push('b')    // this is what works

        scope.$apply()

        // Now if we ran option a) the UI is not updated
        console.log(scope.value) // prints ['a', 'b'] however
        // But when this function is called the next time
        // the value of scope.value has switched back to ['a'].

        // If we ran option b) instead, the UI is updated
        console.log(scope.value) // prints ['a', 'b'] as expected
        // The difference is that the value of scope.value is
        // still ['a', 'b'] the next time this function is called.
    }
}

So the question here is that why can't I change the object the scope is pointing at? But I can modify it instead?

The SecondService contains another function called by another directive, using the same scope. And in that function I can perform the operation I want - which is replacing the current array with a new one.

The only reasons I can think of are some sort of race conditions.

----- Edit -----

I think I'm starting to catch the problem here. The scope object I have in the SecondService is only a pointer to the real scope object.

scope.value ------> [array]
scope.atSecondService --------> scope.value -------> [array]

So when I change the array at scope.atSecondService this is what I get:

scope.value ------> [array]
scope.atSecondService -----> [newArray] <---/--- scope.value

This still makes me wonder, though, that why can I call a similar function from another directive where this works?

----- Edit 2 -----

Or maybe I'm wrong. The behavior is not consistent. It seems like I get a new local level scope created at the element level instead of accessing the $scope at the controller. However, the first time I receive the scope it's the controller's scope - that's confirmed from its value.

Maybe someone else knows better?