I read somewhere "an option on the role for inheriting privileges within AROs defined in the class hierarchy. Selecting this option provides the user with all privileges in the class hierarchy for AROs and user roles."
So with that said, is this statement holds true for runtime behavior ? as i do not see anything changing in design time with/without checkbox checked.
As far as I know the setting is an aid to developers / designers to define RARO ( access role objects) within a class hierarchy more easily.In your case say, you had selected the checkbox and defined the privilege in the parent class only, and tried to create an instance of the child class. I believe depending on the role you have set in the user access group profile , this setting would ensure that the right privilege is first searched in the child class and if not found then it is automatically starts looking up the class hierarchy for the privilege rule.
What you can also do is define the privilege in both the classes in the RARO , but if the access setting is same then it makes sense to use the feature of inheritance.
The setting allows privileges to be inherited, as described above by Anoojit. Consider the use case where an ARO is created in a more specific class using the same privileges as the ARO applied to the generic class. If the setting did not exist, all the privilege settings for the ARO in the more specific class would have to be duplicated. The checkbox saves time and also reduced the probability for error.