Virgin Trains has questioned footage showing Jeremy Corbyn sitting on the floor of a "ram-packed" service.
In a film shown on The Guardian, the Labour leader said he was experiencing a problem "many passengers face every day" on the London to Newcastle train.
But Virgin said CCTV showed Mr Corbyn and his team walking past available seating before starting filming.
It says the crew helped him to a carriage where seats were available and he sat for the rest of his journey.
According to The Guardian's report last week, the footage of the Labour leader was taken by Yannis Mendez, a freelance filmmaker who volunteers for his campaign.
The Labour leader chose the spot on the floor instead of upgrading to first class, it said.
In the footage, Mr Corbyn said: "This is a problem that many passengers face every day, commuters and long-distance travellers. Today this train is completely ram-packed.
"The staff are absolutely brilliant, working really hard to help everybody.
"The reality is there are not enough trains, we need more of them - and they're also incredibly expensive."
Mr Corbyn said the episode made the case for the railways to be renationalised, one of his key policy pledges.
How Virgin says the journey unfolded
He had been travelling to Newcastle to take part in a hustings against Owen Smith, who is challenging him for the leadership of the Labour Party.
Virgin founder Sir Richard Branson tweeted a link to the CCTV images, saying Mr Corbyn had "walked past empty unreserved seats then filmed claim train was 'ram-packed'".
The company said that after Mr Corbyn's team had finished filming: "The same footage then shows Mr Corbyn returning to coach H and taking a seat there, with the help of the onboard crew, around 45 minutes into the journey and over two hours before the train reached Newcastle.
"Mr Corbyn's team carried out their filming around 30 minutes into the journey."
It said the first stop on the journey, on 11 August, had been York - 1:50 hrs after leaving London.
Mr Corbyn's campaign team said: "When Jeremy boarded the train he was unable to find unreserved seats, so he sat with other passengers in the corridor who were also unable to find a seat.
"Later in the journey, seats became available after a family were upgraded to first class, and Jeremy and the team he was travelling with were offered the seats by a very helpful member of staff."
They released photos of other people sitting on the floor and comments from a fellow traveller who said the service was "very overcrowded".
Asked about the CCTV footage apparently showing Mr Corbyn walking past seats without "reserved" signs on them, the Labour leader's team said some of these seats had bags on them which appeared to belong to people who had gone to the toilet.
Analysis by Tom Bateman, BBC political correspondent
On one level, this is a story that appears trivial - about whether a politician could find a seat on a train.
But it is fast developing into a political row between the leader of the opposition and one of Britain's biggest rail firms.
Jeremy Corbyn's video on the floor of the train made a political point - that the "ram-packed" train showed the case for the renationalisation of the railways.
Here was a Labour leader attacking the performance of private train companies in a vivid and visual way. The response: Richard Branson today tweeted the claim that Mr Corbyn had walked past empty seats - complete with CCTV picture.
Team Corbyn's statement appears to add another perspective about events on the 11:00 Kings Cross to Edinburgh: That other passengers sat on the floor too.
It will be important for a leader who promised a "new kind of politics" and authenticity not "spin" - his opponents would waste no time attacking him if they believed the video was stage managed.
At a leadership rally in east London, Sam Tarry - Mr Corbyn's campaign spokesman - accused the Virgin boss of taking a "pop" at the Labour leader for challenging the status quo.
He said the "spat" illustrated that the "establishment is absolutely petrified at what this campaign and what this movement is all about" - adding that Labour's commitment to renationalise the "failed" railways had "great resonance" with the public.
Virgin Trains, which runs the service as part of its East Coast franchise, thanked Mr Corbyn for his praise for its staff and said more capacity was being introduced at peak times.
The operator told Press Association that two passengers were moved from standard to first class so that Mr Corbyn could sit next to his aide.
It added: "But we have to take issue with the idea that Mr Corbyn wasn't able to be seated on the service, as this clearly wasn't the case.
"We'd encourage Jeremy to book ahead next time he travels with us, both to reserve a seat and to ensure he gets our lowest fares, and we look forward to welcoming him onboard again."
On Twitter, Mr Smith said his campaign remained "on track" and that he was "proud to be genuinely standing up for ordinary people".
The Transport Salaried Staffs Association said Virgin Trains was being "disingenuous", claiming the empty seats were in fact reserved.
Manuel Cortes, the union's general secretary, said: "Passengers fully empathised with this story because far too many of them are having to put up with the sort of travel that Jeremy was right to highlight on a regular basis and have had to pay through the nose to do so.
"No amount of spinning by Virgin will dent the people's will to see our railways brought back into public ownership."