The family made the assertion at Standard Performance, Chuwong's construction company, where they called a press conference yesterday (August 3).
The family lawyer, Anek Khamchum, said footage from a surveillance camera showed Chuwong being driven off in a Lexus sports utility vehicle from Chuwong's company on June 26, hours before the vehicle crashed into a tree on Chaloem Phrakiat Road in Prawet district.
The Lexus that left the company is believed to have been driven by former deputy commerce minister Banyin Tangpakorn.
In the footage, the Lexus pulled over by the car park of Standard Performance and Chuwong got inside.
He is seen reaching for the seat belt and fastening it before the vehicle drove off.
Mr Anek said it was Chuwong's habit to keep his seat belt on at all times while travelling on the road.
The autopsy results showed Chuwong bled to death through injuries sustained to his head and swollen brain caused by his head hitting something hard.
There were also deep bruises on the back of his head. The injuries suggested Chuwong was not restrained when the crash occurred.
After leaving the company, Chuwong was thought to have headed to a golf course where he played before leaving in the same vehicle in the afternoon. He was later involved in the car crash, which left Chuwong dead in the passenger seat and Pol Lt Col Banyin, who drove the vehicle, slightly injured.
Mr Anek said police were also reviewing more footage obtained from a camera at the golf course.
Wanpen Thanathammasiri, Chuwong's elder sister, said Chuwong always wore a seat belt, whether he was driving or in the passenger seat, after he had survived two serious car accidents in the past.
Turning to the share transfer issue, Ms Wanpen denied knowing the two women who received substantial amounts of stock from Chuwong.
Ms Wanpen said the family had never met the women before, which was contrary to a statement which a witness had given to police, understood to be Pol Lt Col Banyin.
The women are Uracha Wachirakulton, 25, who worked as a broker for Chuwong's stock trading account, and Kanthana Siwathanapol, a golf caddie at the Lakewood Country Club on Bang Na-Trat Road.
According to police, Chuwong transferred about B30 million worth of stock to Ms Uracha, through her mother's account.
Ms Uracha and Ms Kanthana reportedly each told police they were in a relationship with Chuwong.
No one has been charged in connection with Chuwong's death.
Ms Kanthana, through her lawyer, Seksan Senachoo, petitioned the Crime Suppression Division (CSD) to unfreeze the shares worth more than B200 million which she received from Chuwong. Mr Seksan said news about the investigation had pushed down the prices of shares in companies in which Ms Kanthana traded.
Police spokesman Pol Lt Gen Prawut Thawornsiri said police found irregularities in the transfer of shares to the two recipients. Certain parts of some important documents had been altered, reportedly with an eraser liquid, where there were not supposed to be changes.
Pol Maj Gen Akradet Pimolsri, the CSD commander, said investigators were examining suspicious alterations in the transfer documents. So far, 20 witnesses have been questioned in the case.
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