No, it isn't bad for amateur or professional athletes. The woman just displays Conventional Wisdom that is not backed up by science.

Since moving to a "sports diet", as I've been training for an event this summer, I have reintroduced starchy vegetables as a daily food - I haven't changed the fats I consume. I don't feel that video was terribly accurate as far as things you should have or not have.

Saturated fats are perfectly healthy for athletes, although not required, they are far better than excess pufa's. Due to their being fully saturated, they are much more stable, less likely to oxidize and are essentially cleaner burning than mono or poly. Also certain saturated fats such as medium chain triglycerides are metabolized differently in the body, and are a great source of energy. Since fats are required, and saturated is the best cooking fat due to its stability and less likely to oxidize, I think a certain amount of them are great in an athletic diet. They are substantially better than the excess pufa omega-6 in the normal SAD diet.

Sat fats are required.