Setting properties of custom class objects that are dictionary values, where the dictionary is a protected property of another class

I am exploring different ways to use OOP in Matlab. I set it up as follows

classdef A_test < handle
    properties (GetAccess = public, SetAccess = protected)
        B
        db
        dc
    end

    methods 
        function obj = A_test()
            obj.B = B_test;
            obj.B.value = 'z';

            obj.db = dictionary;
            obj.db(1) = B_test();
            obj.db(1).value = 'x';

            obj.dc = dictionary;
            obj.dc(1) = C_test();
            obj.dc(1).set_value('y');
        end
    end

end

classdef B_test < handle

    properties (Access = public, SetObservable, Dependent) 
        value
    end

    properties(Access = private)
        value_
    end

    methods
        function val = get.value(obj)
            val = obj.value_;
        end

        function obj = set.value(obj,val)
            % input checking
            obj.value_ = val;
        end

    end
end

classdef C_test < handle

    properties (Access = public) 
        value
    end

    methods
        function obj = C_test()
            
        end

        function obj = set_value(obj,val)
            % input checking
            obj.value = val;
        end

    end
end

I am able to set A.B.value, but A.d(1).value throws an error (but it actually does set the value successfully):

A.d(1).value = 'z'
Unable to set the 'd' property of class 'A_test' because it is read-only.

I think this is because the dictionary tries to update its hash table when a value changes. However, the third way, C_test, works with no errors, so that doesn't totally make sense. What is going on here? I would like to use B_test if possible.

Edit: Code to run the test cases:

A = A_test();
A.B.value = 'q';
A.B.value

A.dc(1).set_value('r');
A.dc(1).value

A.db(1).value = 'p';
A.db(1).value

[Matt J]

Please include code that executes the test. How was A created? Where do you attempt the assignment? In the base workspace?

[sigguy90]

@Matt J Sorry, I included the test execution code now. I believe I am in the base workspace.