Police quickly informed Venus Williams she was "at fault" in her fatal car accident, but also explained why she wasn't being cited -- namely that she got "caught in the middle."

Palm Beach Gardens PD released the full bodycam footage from officers on the scene of the June 9 accident. One officer approached Venus and asked her to describe what happened.

She was totally upfront with the officer ... explaining how she had entered the intersection, but stopped when another vehicle made a left in front of her.

The cop told Venus he believed she had violated the right of way of Jerome and Linda Barson -- the couple who T-boned her -- but she would not be getting a ticket. The explanation? "I think you got stuck in the middle of the intersection. It's one of those situations where you had the right way, but you lost the right of way."

His advice to Venus ... let the insurance companies sort it all out.

The bodycam footage also includes the Barsons sitting in their Hyundai, waiting for treatment. Their airbags had deployed and they were clearly shaken up. As we reported ... Linda suffered several broken bones, while her 78-year-old husband, Jerome, was hospitalized for 2 weeks before he died from his injuries.

SPEAKING TO THE VICTIM
TMZ.com