It is fairly common for such TV programmes to be inaccurate/untruthful. Perhaps journalistic licence?
About a dozen times a year you will hear that incident at Parkside, (death of William Huskisson) was the first rail fatality. It was certainly significant, the first WIDELY REPORTED death, but first death? Well only if you ignore the numerous deaths on Stockton-Darlington railway: "In 1828 two locomotive boilers exploded within four months, both killing the driver"! And these were not the only fatalities. Also there had been fatalities on the less publicised colliery lines! Interestingly, the S&D had a similar accident on their opening day, though on that occasion the victim survived with a crushed foot!