Pretty sure the police said he shot first.
Well, for the officers involved, distortion of perception can be one of the psychological and physiological effects of stress. Or they could have lied. I ain't judging either way. That's why we have investigations to determine whether shootings are justified or not.
On the PR front, I'll never deny that police forces tend to have fucked up, confused, or amateur messaging in situations like these. It's not our strong suit.
Of course, if the Met releases no info at all pending the investigation, media types cry coverup. If they try to get out in front of the story and release what they know/believe initially, they get roasted if later info says the initial info was inaccurate. Can't win.