OK, so I consider the question of whether parents cause eating disorders to be clear: no we don't.
But can we prevent them?
I do not consider the symptoms to be the cause or their absense to be the absence of an eating disorder.
In other words, if you are built to respond that way to inadequate or erratic nutrition you will have those symptoms no matter why or how you are undernourished. Therapy and insight and a different environment may help you avoid or cope better but they don't make your response to malnourishment change. And: if you are not undernourished those symptoms need not be part of your life at all.
Of course there are often co-morbid issues that drive malnourishment and make it a struggle to maintain normal nourishment. There are copious social and personal reasons a person may struggle to do so as well. But the illness itself is a paradoxical brain/behavior response when undernourished.
Yet I do think we play a possible role in preventing the onset of symptoms and an enormous role in stopping them once we know about this paradoxical brain problem.
I have wondered over the years whether a different family style around meals might have been protective for our daughter. I have wondered if my own growing dismay over my own weight gain during the years around our daughter's adolescence might have provided fertile ground. I also look at certain personal and international events and wonder "what if they hadn't happened and we hadn't had all that heightened anxiety in the house during that year?"
What I do know is that I'll never know. I'm also confident that the recipe for an eating disorder is unlikely to be that direct and obviously the same dish can have a number of recipes. I am dead sure that the greatest problem in the months after the diagnosis was my own confusion about these factors: they led to distraction and self-involvement instead of action and good sense.
If I could go whisper in my own decade-back ear now, I would recommend slightly different parenting, different modeling, and a higher sense of risk from events that seemed not to be as important at the time. I would go back and erase my own attempts at weight control, every time that I didn't speak up at a fat joke, and my buy-in to the belief that it was "healthy" to avoid certain foods and it was "normal" for a high school kid to skip breakfast and have track practice through dinnertime.
I would change those things not because they "caused" the problem, but because they messed up our response to the situation. What strikes me about the ubiquitous "prevention" advice to parents is that it implies a straight line and a dose-response: a little influence a little eating disorder, a lot of influence a very serious eating disorder. THAT kind of thinking about eating disorders is what I really, really wish we could prevent.