Coulson didn't put The Sun back in their box.
The Sun claimed a TV presenter had committed child sexual offences.
They had no evidence to support that and the alleged 'victim' had contacted them telling them there was 'no truth' to the article they were about to publish.
The Sun went ahead and published.
After being ignored, the alleged 'victim' employed lawyers to publicly state their position.
After a week of desperately trying to come up with some dirt on the TV presenter, The Sun came up with very little so backed off.
Andy Coulson had nothing to do with the public perception of how this entire case has been perceived.
Anyone with any sense can see The Sun f-up and that's has zero to do with Andy Coulson.
And zero evidence till now that he's using some kind of amazing PR.
IF Andy Coulson is involved in PR for Huw Edwards there's nothing so far that could be considered to be 'spin'.