Generally, countries do initially investigate themselves because it’s actually one branch of management investigating someone who reports to them.
If this were the UK and there were allegations of war crimes against army personnel, I would expect the army to do that investigation. Then I would expect the government to investigate the army and if that is not satisfactory then you’d expect external bodies to investigate further.
The problem here is that the crimes have the backing of the higher ups so steps one and two aren’t about whether a crime had been committed but about how they deny the accusations?