While the fashion show that led to Prince William and Catherine Middleton becoming a couple and the Queen Mother's death did not actually happen the same day, they did happen in close proximity to one another. The fashion show was March 26, 2002 and the Queen Mother's death occurred on March 30, 2002.
While Operation Paget debunked the conspiracy theories promoted by Mohamed Al-Fayed regarding the deaths of Diana and Dodi, Sir John Stevens never delivered a public speech to that effect. Al-Fayed also never left the UK following the inquiry.