Points to note:
A radiator that is hot at the top CANNOT ever be caused because it needs bleeding. Its a simple case of physics - gas sits at the top preventing the hot fluid reaching the top.
Black sludge can form very quickly in a system with no inhibitor installed - certainly inside one year. If the system is short of inhibitor (below the recommended strength), the rate of sludge forming will be less, but will still occur over a longer period. You cannot overdose the inhibitor - only underdose.
I agree with Jomifl answer, apart from his assertion that "there wouldn't be that much sludge after 4 years" - it isn't time dependent, it is time and underdose dependent.