Jeremy Clarkson sported a large scab on the side of his nose in this week’s episode of The Grand Tour. It was never explained whether it was the result of a stunt or a supper order gone wrong. But, of the three episodes in Clarkson’s comeback released so far, this one seemed most intent on giving the BBC a bloody nose.

One of the freedoms Clarkson and his producer Andy Wilman have in their new travelling home – this week, they pitched their studio tent in Whitby – is that episodes can vary in length: the third was 62 minutes, up from 57 in the second but significantly down from the 71 of their online debut.

But the latest episode would struggle to fill even a half-hour slot on the BBC, once it had been shown to the Head of Editorial Compliance. Challenged by Hammond and May for using the word “prick-teaser” about BMW, Clarkson perkily offers “cock-teaser” as a substitute. The description of part of a dashboard resembling “a lady part” would surely have been deleted at his old address. Much scrutiny, too, would be given to the trio’s expensive watches seen prominently on steering wheels. (“Episodes contain product placement,” warns the Amazon Prime website.)

Intent on giving the BBC a bloody nose … The Grand Tour. Photograph: Ellis O'Brian

This instalment also contained a gag that seemed openly aimed at the failure of the BBC’s replacement Top Gear. During a sequence filmed in Italy, Hammond was obsessed with doing “doughnuts”, dirtily circling a car in a Florence square and later doing ovals in a speedboat in Venice lagoon while Clarkson and May look on, horrified, from a gondola.

One of the first of many crises that engulfed the post-Clarkson Top Gear was accusations of “disrespect” after Matt LeBlanc drove spheres of burnt rubber into a road close to the Cenotaph in London. The decision by Chris Evans to publicly disassociate himself from the sequence seemed to create tensions between the two, a perception that helped to crash the franchise.

At first sight, the wheelie stunts in The Grand Tour look like a bid to culturally out-vandalise LeBlanc. Hammond seems to be scorching the stone directly outside the Uffizi gallery, and surging through Venetian waters that are a UNESCO World Heritage site. Careful viewing, though, suggests that skilful filming and editing have been used to confuse viewers about what they are really seeing.

Mobbed in Tuscany … the presenters’ Italian job. Photograph: Ellis O'Brian

One of the difficulties the Clarkson-Wilman Top Gear faced at the BBC was that – following a series of scandals on other shows about editorial deceits – all programmes were held to factual standards that had previously been applied to news and documentary. This hampered Clarkson, Hammond and May, who had always employed elements of misleading, teasing and even fiction.

On The Grand Tour, the team is again allowed to be playful with form and facts, in the way Top Gear once was. If Amazon Originals even has a Head of Editorial Compliance, they seem to be no more bothered than most viewers about whether Hammond and May really are destroying Clarkson’s house with bulldozers (a pay-off from a bet in show one), or that a scene in which the other two are trying to strand Hammond at a hotel is clearly scripted.

Let loose online, there are elements of misleading, teasing and even fiction … Hammond and May bulldoze Clarkson’s house. Photograph: Ellis O'Brian

So much does The Grand Tour stray into drama that the presenters’ Italian job was based on the premise of Clarkson (whose career is built on being a man of the people) being a culture vulture whose desire for opera and art in Tuscany is thwarted by Hammond’s vulgar tastes. But Clarko’s sophistication didn’t prevent him accidentally going to see an opera that he believed to be called Car Men, and therefore up his street.

Such creative licence still leaves space for proper motoring journalism: they mock the Rolls-Royce brochure that describes the removal of its convertible’s roof as a “silent ballet”, and Clarkson suggests that the boasted extra head-room in a VW SV makes it “like a Golf but for people who have stovepipe hats.” Few factual shows pay such attention to language.

Regardless of how many new online shoppers The Grand Tour may have attracted to top up Amazon’s tax-lite profits, this is a television event. Many will flinch as Clarkson progressively tests his claim in programme one that “this is on the internet – I can’t be sacked.” But The Grand Tour is inventive, expensive, authoritative programme-making that is luxuriating in fresh editorial freedom.

If something needs to be looked at in future, it’s the structure. It seemed odd this week that the base location of Whitby was used almost entirely as a movie theatre for the Italian job. Stranger still was no mention of the fact that Whitby is a key location in Bram Stoker’s Dracula – possibly because the main character reacts even more violently than Clarkson once did when struck by hunger.