As part of its explanation of the stewards' decision, the FIA said that Webber did not have permission from the marshals to go onto the track, and that this was the key element in the decision to punish him.
AUTOSPORT understands that in the marshals' report issued to the stewards they stated that instructions were given to Webber for him not to enter the track. However, Webber may not have heard them over the noise of cars as he was already running towards the circuit.
The regulations demand that drivers can only go on track if they have permission from marshals.
ANALYSIS: Why Webber was penalised
Webber took to his Twitter account on Tuesday morning to criticise the ruling and insist that he had not heard the marshals' instructions.
CCTV footage issued by the FIA showed marshals at the corner gesticulating at Webber to stop.
"For @alo_oficial [Alonso] and me to receive reprimands for our actions after the race it is comical to say the least," he wrote. "Great moment, and fans loved it.
"And while I'm at it, contrary to reports, there was no interaction at all with any track officials after we put the fire out."
Alonso was also reprimanded as the race officials judged that he had stopped in a dangerous manner when he collected Webber.
As Webber's reprimand was his third of the year, he automatically received a 10-place grid penalty for the next race in Korea.
AUTOSPORT revealed on Monday that the FIA would now advise Formula 1 drivers not to give stranded rivals passenger rides in the manner Alonso had with Webber.
Both Webber and Alonso mocked the decision on their Twitter feeds during Tuesday.
Webber retweeted a photo montage of other F1 driver taxi rides from history, and drew attention to Singapore GP stewards' driver representative Derek Warwick riding on Gerhard Berger's Ferrari in 1988, while Alonso tweeted a mocked-up poster for the film Taxi featuring his and Webber's faces.
Warwick insisted to the Daily Telegraph newspaper that it was not the taxi ride itself, but the manner in which Webber went onto the track and Alonso stopped that resulted in punishments.
"It is not health and safety gone mad," said Warwick. "A driver could easily have been hurt. I hope we're not seen as killjoys.
"I want Formula 1 to be entertaining. I want it to be a spectacle. I'm a big fan of MotoGP and I wish we in Formula 1 could get closer to the drivers like they do in MotoGP.
"We have become a bit sterile in many ways in Formula 1. But we cannot put drivers at risk.
"If it had been done in a safer manner then it might have been viewed differently, but this was potentially very dangerous. You can't have cars parked in the middle of a corner."