If you accept this to be true, how do you fit Mitochondrial Eve into the scenario?
How does it not fit into this scenario? For every gene there will be a most recent common ancestor (MRCA), and they will undoubtedly be different MRCA's for many genes. Our genomes are undoubtedly made up of DNA that was not found in ME but was found her contemporaries.
Let's use language as an example. There are many different words in the english language. It would be incorrect to trace the origin of a single english word and date the origin of the entire language based on the origin of that single word. And yet, this is exactly what you are doing with ME. Our mitochondrial genome is but a single piece of our entire genome. There are many different points of origin for different genes just as there are many different points of origin for different words in the english language.