That is not correct. Copyright subsists in all original works of authorship fixed in any tangible medium of expression. www.law.cornell.edu/uscode/text/17/102

Legally, when you write your shopping list, you instantly have the rights to that work, no publication or registration necessary. You can choose to publish it later, or not at all, but you still own the rights. Someone can’t break into your house, look at your unpublished works, copy them, and publish them like they’re their originals.