Quaid's comments come a few days after the film's producer, Gavin Palone, wrote about the footage for The Hollywood Reporter.
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He claims that different footage from the rehearsal shows the dog willing to jump into the water when it was on the left side of the pool, as opposed to the right side in the TMZ video, and that the dog was never actually forced into the water.
However, Palone admits that the dog, Hercules, was forced under water for a few seconds by the current, and the producer was not actually on set at the time.
Last week, the film's Kiwi star KJ Apa posted a statement to social media defending the movie, saying he would never attach himself to a project that didn't "treat animals with the utmost care", though added the possibility of such an incident was "troubling".
A Dog's Purpose is still set to screen in New Zealand on April 13. The movie premieres in America this week.