The dog trainer should have stopped trying to get the dog to go in the water as soon as the dog seemed uncomfortable, and the trainers should have had support under the dog as soon as he came to the side of the pool and/or had less turbulence in the water so he never would have gone under.
These two things are absolutely INEXCUSABLE and should NEVER have happened.
As with the TMZ video that you saw, two things were evident: 1) the dog handler tries to force the dog, for 35 to 40 seconds, into the water when, clearly, he didn’t want to go in; and 2) in a separate take filmed sometime later, the dog did go into the water, on his own, and, at the end, his head is submerged for about 4 seconds.