"The paparazzi themselves corroborate that there was some questionable driving going on"
According to the report in The Times, the 'questionable driving' was from H & M's security:
Witnesses, the couple’s taxi driver and police officials have cast doubt on their initial description of events, with some disputing that lives were at risk.The photographers accused of driving dangerously went further, claiming that the duke and duchess’s team were the ones being irresponsible behind the wheel.
One paparazzi driver involved in the pursuit has countered the claims of the duke and duchess. He blamed the couple’s team for any “catastrophic experience” they had, telling ITV anonymously that their driver was at fault for “zigzagging” and “blocking” vehicles. A celebrity news agency claiming to hold video of the pursuit echoed his observation.
The agency (Backgrid) accused the driver of “one of the four SUVs from Prince Harry’s security escort” of “driving in a manner that could be perceived as reckless”.
It said: “The vehicle was seen blocking off streets, and in one video it is shown being pulled over by the police.”
Another witness came forward to say that the couple’s team had been taunting the photographers. “They were mocking the paps, provoking them,” the witness told the New York Post. “These security egged on the paps.”
HERE is a link to the full article in The Times, which has a detailed timeline of events.