The cell theory states that living things are composed of one or more cells, that the cell is basic unit of life, and that cells arise from existing cells. A component to the cell theory is that the cell is the basic unit of life.
it is accepted that cells contain DNA in chromosomes and RNA in the nucleus and cytoplasm, but only in the modern cell theory. the classical cell theory does not include this. but using either classical or modern theory, it is false that all cells have DNA surrounded by a nucleus.