A new twins study from UK suggests picky eating is 78% genetic. The remaining 22% influence is from raising genetically similar kids differently within the same household. So, if you raise genetically unrelated kids in the same household, they're no more likely to be similarly picky (or not) than if they'd been raised in different households.
I always believe my kids' pickiness is my fault for failing to shop or cook properly. Now I think my kids' pickiness is my fault for giving them picky genes.