I believe the debunking is that there's good evidence many of the participants realized they were in an experiment and the other person was an actor, but Milgram hid this in order to get a famous paper.
You'd start by telling yourself that, so it would be easy enough to convince people looking to "debunk" the experiment later.
The new research builds upon findings from a previous study, which analyzed recordings of 91 conversations conducted immediately after the termination of the experiments. The recordings showed that most of the obedient subjects justified continuing the experiment because they believed the learner was not really being harmed.