What Barry says could be correct, but I doubt Mr Kubrick would show anything that goes against proven science. The conditioning shown in this movie is also known as Pavlovian conditioning. In short, Pavlovian conditioning says that once your mind is conditioned to perform certain activities in the presence of certain stimuli (external or otherwise), it will continue to do so involuntarily.
Read the the Pavlov dog experiment for more details.
In this movie, the example would be the scene when Alex throws while indulging in violence after the conditioning is complete.
So I think, that when Alex says 'I was cured alright', he means that even though he is willing to continue his violent lifestyle (read conscious remains uncured) he cannot do to so because his body betrays him (read subconsciously cured (from society's perspective of preventing violence).
Just my tuppence worth.