Why is that unscientific? It's well known that cast iron gets "seasoned" by what you put in it, so if you put crap in it it's going to get seasoned with crap.
I'd say it's unscientific because it includes an unfounded / somewhat superstitious implication that non-organic flaxseed oils contain toxic chemicals. Less notable, the author casually misuses "leach."
Sure, but she seems to be assuming that flaxseed oil pressed from organic seeds must necessarily be more pure than oil pressed from non-organic seeds. I'm not sure what the reasoning is... organic seeds wouldn't necessarily have been treated with any less pesticide, for example. The "organic" label often just means that the soil was fertilized with nitrogen from sources like manure, rather than nitrogen fixed from the air... but it's still just nitrogen.