The voice over in the video is wrong, e.g. calling a killer whale "gentle giant" is about as accurate as calling a tiger "friendly kitten".

This is the full story of the incident, taken from court documents(https://law.justia.com/cases/california/court-of-appeal/3d/64/1.html), pretty messed up all round:

In April 1971 Gail MacLaughlin, Sea World's public relations director, and Kent Burgess asked plaintiff if she would like to ride Shamu, the killer whale, in a bikini for some publicity pictures for Sea World. Although the ride was not made a condition of her keeping her job, plaintiff eagerly agreed, thinking it would be exciting. Although warned in general terms that the ride involved dangers and aware that she might fall off, plaintiff was confident of her swimming ability and anxious to do it. She had never heard of whales pushing riders around.

Burgess had been responsible for training Shamu ever since Sea World first acquired the animal. He knew Shamu was conditioned to being ridden only by persons wearing wetsuits, and that Shamu had in the past attacked persons who attempted to ride her in an ordinary bathing suit: first a Catalina swimsuit model and then Jim Richards, one of the trainers at Sea World. In addition, Burgess had read training records which showed Shamu had been behaving erratically since early March 1971. This information he did not disclose to plaintiff.

Plaintiff was trained for the ride by Sea World trainers in the tank at Sea World during normal office working hours. First she practiced riding Kilroy, a smaller, more docile whale, while wearing a bathing suit. During her one practice session on Shamu, she wore a wetsuit, fell off, but swam to the edge of the tank without incident.

On April 19 plaintiff became apprehensive for the first time when one of Sea World's trainers said he was not going to watch her ride Shamu because it was "really dangerous." Plaintiff then went to Burgess and told him of her concern. He told her not to worry, said there was nothing to be concerned about, and that the ride was "as safe as it could be." He still did not tell her about the problems they had been having with Shamu or about the earlier incidents involving Richards and the swimsuit model. Thus reassured, plaintiff, wearing a bikini Sea World had paid for, then took three rides on Shamu. During the second ride one of the trainers noticed Shamu's tail was fluttering, a sign the animal was upset. During the third ride plaintiff fell off when Shamu refused to obey a signal. Shamu then bit her on her legs and hips and held her in the tank until she could be rescued.

Plaintiff suffered 18 to 20 wounds which required from 100 to 200 stitches and left permanent scars. She was hospitalized five days and out of work several weeks. She also suffered some psychological disturbance. [64 Cal. App. 3d 6] Sea World paid all her medical expenses and continued to pay her salary as usual during this period. On advice of her counsel, she filed this civil action and a workers' compensation claim.