An increasingly bitter fight between Tesla and its former autopilot partner Mobileye is raising questions over the electric car company's honesty.

Elon Musk's corporation is notoriously prickly. When it does come under criticism – whether on safety issues, the practicality of long-distance drives, or its autopilot feature – its first response is to lash out.

In the latest exchange between Mobileye and Tesla, however, the chip company has accused Tesla of lying. "The allegations recently attributed to a spokesperson for Tesla ... are incorrect and can be refuted by the facts," Mobileye said in a statement.

Late last week, Tesla argued that it had ended its relationship with Mobileye – for autopilot chips and software – because Mobileye demanded Tesla end its research into its own image-sensing systems. According to Tesla, when it refused, Mobileye said it would no longer support its hardware.

Mobileye tells a very different story.

It ended the relationship in July, it says, and the reason was Tesla's willingness to extend its own risk-taking culture to its customers.

Tesla was "pushing the envelope in terms of safety," the company's chairman and CTO Amnon Shashua said in an interview with Reuters on Wednesday. "It [the autopilot system] is not designed to cover all possible crash situations in a safe manner ... It is a driver assistance system and not a driverless system," he said.

Interesting use of 'auto'

At the heart of the issue is Tesla's excited promotion of its driver-assistance systems as an "autopilot" – and the subsequent fatal crash of 40-year-old Joshua Brown in his 2015 Tesla Model S while driving in Florida in May.

Since the crash – which played into everyone's fears about cutting-edge car technology not being safe – Tesla has provided a number of different explanations of the cause. An official investigation into the crash is not expected to formally report for another ten months.

While the assisted-driving technology is undoubtedly impressive, Mobileye says it was very unhappy when Tesla started suggesting it would allow customers to drive their car hands-free. Brown was thought to be watching a movie when the crash happened.

"It has long been Mobileye's position that Tesla's Autopilot should not be allowed to operate hands-free without proper and substantial technological restrictions and limitations," said the company's most recent statement, adding: "In communications dating back to May 2015 between Mobileye Chairman and Tesla's CEO, Mobileye expressed safety concerns regarding the use of Autopilot hands-free."

At first, Tesla pinned the blame for the crash on the car's camera not being able to tell the difference between a white trailer and a bright sky – in effect shifting the blame from its own systems to those provided by a third party. Guess who that third party was?

"Tesla's response to the May 7 crash," notes Mobileye, "wherein the company shifted blame to the camera, and later corrected and shifted blame to the radar, indicated to Mobileye that Mobileye's relationship with Tesla could not continue."

It goes on: "Failing agreement on necessary changes in the relationship, Mobileye terminated its association with Tesla. As for Tesla's claim that Mobileye was threatened by Tesla's internal computer vision efforts, the company has little knowledge of these efforts other than an awareness that Tesla had put together a small team."

Mobileye claims that after the crash, it had a face-to-face meeting with Musk in which he promised that the autopilot would be "hands on." But then Musk reneged on the agreement, it says, and offered a hands-free activation mode.