On the Ancestry site, their FAQ says "Your DNA test results also provide information that’s more relevant and recent—targeting your family history a few hundred or even a thousand years ago". This statement helps to clarify why genealogy doesn't equate to DNA results.

To use an example related to the OP's, all of my great grandparents are born in the United States. However, that doesn't mean that I'm genetically 100% American. The data points used to construct Ancestry information come from many distinct times, and grouping will depend on an individual's SNP or indel (insertion/deletion) at a particular point in the genome.

For instance, at a particular location in the genome, a specific DNA base "A" might be associated with some French population, while a "G" or "T" at the same position might be associated with a distinctly German population. These represent specific alleles or variants at a particular time point. The collective set of alleles Ancestry has information on will come from a huge range of time, as suggested in the FAQ response cited above. Thus, the test gives you a representation of your history from many different periods and generations, but doesn't generate a neat delineation of genealogical information.

For more information, and other issues that can arise, here's this link.