If I wore an apron like that to bake cookies, the ONLY way it could catch on fire is if I took a stick and poked the ends down into the bottom of the oven where the flames are. It's really not easy to get to naked flame, at least not in my stove and I think my stove is a pretty average/normal stove. Range top cooking...why would you lean your body over a lit range in the first place? Wouldn't your boobs catch on fire, strings or no strings? LOL
I've cooked in a lot of floppy outfits, hunching over large open flame (campfires) and no problems. I'll wrap my sleeves over my hands and shove my arms right into the flames to grab a pan...never had a problem. I wear cotton almost exclusively (wouldn't reach into a fire with polyester on) and it just doesn't seem to catch on fire very easily.
I don't understand why this apron would be significantly more dangerous than any other apron for cooking in your average kitchen. Working with machinery, I would definitely see the danger. But for cooking on modern appliances...I don't get it.