That conclusion was drawn too hastily; the aesthetic appeal of a dichotomy was too great. Simply because there are two types of cell at the microscopic level it does not follow that there must be only two types at the molecular level.
The evolutionary relation of prokaryotes and eukaryotes is actually more complicated than the evidence cited above would indicate. Two eukaryotic organelles, the mitochondrion and the chloroplast, each have their own DNA. Moreover, the pigments in the chloroplast (the chlorophylls and the carotenoids) are similar to those found in the cyanobacteria. Both mitochondria and chloroplasts are the size of bacteria; their apparatus for translating genetic information into proteins differs from the eukaryotic cell's own apparatus and has a number of properties in common with that of prokaryotes.