It’s a bit of a strange one, this. I understand what they are trying to say: governments perform executions only because people acquiesce in them (don’t oppose them) or because they actively approve of them (this approval can be intellectual or moral, or it can manifest itself through active participation as viewers in the process of a public execution). If the public were to turn their backs on the whole affair – not because of apathy or acquiescence but because of opposition - then capital punishment would probably disappear, even in non-democratic states.
However, the image used here conveyes the opposite: people turn their backs, and governments are left in peace to carry on. In light of the massive presence of people at the scene, they could easily stop the execution if they had not decided to turn away.
But perhaps I’m reading this the wrong way. Other interpretations are welcome.