Just look at this. It doesn't look like it's making contact...
Well, Petal Dance isn't Physical.
Petal Dance is Special.
Basically, you are shooting petals at a target. Those petals have to hit the target to hurt it, right?
Anime doesn't really relate to games. And I think that image was part of a Bulbasaur who participated in a Pokemon Contest. Plus, it is Special, not Physical. Meaning the Leaves in the image will hit the foe, but without the use of the body.