The following apology was added to this article on Thursday 18 March 2010

This article was amended on Monday 15 March 2010 to delete a reference to comments reportedly made by Peter Vaughan, the Chief Constable of South Wales Police, in an interview with Police Review about his personal security. Police Review has since accepted that Mr. Vaughan did not make those comments and has apologised for its mistake. We apologise to Mr Vaughan for any embarrassment caused.

"I have spoken to the officers ­concerned and reminded them in no uncertain terms that _______ ______ ____ is a very bad idea should they wish to progress under my command." Can you fill in the blanks in this statement from Superintendent ­Andrew Murray, Oxford City commander with Thames Valley police? Like a fiendish spot-the-ball competition, I'm afraid it defies all reason and logic, so those of you who guessed "claiming the suspect kicked himself down the nick stairs" will be disappointed.

The missing phrase is in fact "tobogganing on duty, on police equipment, and at taxpayers' expense", and the public reprimand was issued after a 39-second YouTube clip was posted showing one of Andrew's boys bombing down a snowy Oxfordshire hillside on his riot shield while several colleagues cheered him on rather sweetly.

There's something so precious about a copper's delight in wintry larks – and yet, how quickly such innocence turns to guilt. Amazingly quickly, all told. To suggest that the haste with which the rebuke was issued is uncharacteristic of Her Majesty's Constabulary is a little bit like saying recent weather has tended toward the nippy – and by now you will have spotted the officers' tactical error. Had they truncheoned the civilian who filmed them to the ground, the unwritten police form book suggests they might have expected tight-lipped support from their superiors, who wouldn't have dreamed of offering so much as a mealy mouthed "expression" of regret until an inquiry by the allegedly independent Police Complaints Commission had completed its glacial progress. At the very least, PC Snow Bunny should have arrested the cameraman under the Prevention of Terrorism Act.

Gallows facetiousness aside, I did wonder for a moment whether the shield-sledging officers were G20 riot police on their peace-and-love roadshow, until struck by the recollection that Oxfordshire lies beyond this tour's London catchment area. Are you aware of this grimly hilarious exercise? After what we might euphemistically style as a few PR howlers, officers from the Territorial Support Group have embarked on a goodwill tour to win back public support. The initiative was announced at the end of last year, after a highly critical report by the chief inspector of constabulary which found that the aggression used at the G20 protests, and the general willingness to deploy officers in riot gear the second anyone so much as raises a placard, had seriously eroded the principle of policing by consent. "We have to accept that the TSG have an issue with their image," conceded the Met's man in charge of public order. Part of the fun would involve getting members of the public to don the full kit and interact with real TSG officers. If anyone has participated in one of these demented-sounding role plays, please oblige me with a withering report.

In the meantime, and speaking of wrongheadedness, we must return to the likes of Supt Murray and ask whether his much-ridiculed response is not, in its own infinitely petty way, as crashingly obvious a failure of leadership as the Met's kneejerk willingness to take its own side against the public whom it is meant to serve. No doubt Supt Murray's rebuke would be supported by the senior police officer's manual – what isn't? – but it's the idiotic inability to distinguish between officers having a bit of fun and the sort of serious breach that deserves a public rebuke that is so self-defeating and so heart-sinkingly familiar. Like the Sussex officer who this week stopped and searched two boys aged 11 and 12, with the grounds for intervention being recorded as "sledging downhill", Supt Murray has shown himself incapable of grasping how policing by consent comes about. Normal attritional service must be resumed.

As the chap who filmed the sledging officers told reporters: "[The police] pulled up and we thought they were going to give us a hard time … You don't always build up the most positive image of the police but they broke the mould. They were chatty and pleasant. It was just nice to see them in that situation."

Ah well. They'll know better next time.

Still, there can be no such doubt about Supt Murray's statement, which seems designed specifically to preserve the image of the police as terminally aloof justicebots. Perhaps the Oxford guv is surprised at the outpouring of contemptuous mirth that has greeted it; perhaps he will console himself with some old chestnut about policing not being a popularity contest. The thing is, though, a big part of is exactly that.