https://www.youtube.com/watch?v=PQwbhE1mEV0
Back when Zoe Kravitz was filming Divergent, she suffered an injury that caused her to get 8 stitches. Was it an action scene? Nope. She told Seth Meyers on Late Night, during a break she went to shoot the breeze with Shailene Woodley in her trailer, when a breeze suddenly shut the door closed on her face. To make matters worse she was wearing sunglasses making the injury so much worse.
The good news she has a story about getting injured while filming an Action film. The bad news is that is more embarrassing than exciting.