Can you develop diabetes if you are not overweight or sedentary, and it doesn't run in the family?

Answer 1

Yes you can -- my friend did and none of her immediate family has it.

Answer 2

Your risk factors are certainly lower than the general population that gets Diabetes. And I would not obsess about it. But be aware those are not the only things that can bring on Diabetes.
For instance, trauma to the abdomen that damages the pancreas can cause the disease. A virus or bacterium that decides to settle in the pancreas can cause it as well. Not to mention all the cancers that can do so too. Modern science has learned an enormous amount about the disease and it's processes, but they by no means know it all.