"It can't be both "badly wrong" yet present "a true picture"."

That's unusually confused fot you Teribus. There's no contradiction,because teh two phrases refer to differet things.

The 45 mimute threat, more expeciaslly as blazoned across the media, with no attempt by the Government to correct this, was badly wrong; Gilligen's story essentially presented a true picture of the fact that the dossier produced by intelligence over-emphasised the claim, that this was not in line with what some people involved in preparing the report believed it should say, and that the Government had played a significant role in ensuring this.

This mistake was in saying "probaly" the Government knew that the report was significantly misleading, where the strength of the evidence woidl niot nhave justified going beyond "possibly".