A very good example comes from India itself i.e. "The Paradox of Indian History" which is the dichotomy between Archeological Evidence (Indus Valley, Ashoka's inscriptions etc.) vs. Literary Evidence (Puranas, Itihasas etc.) Add to this the linguistic diversities, group/ethnic diversities and successive waves of invasions and displacements and it is enough to drive a Historian mad/happy depending upon how you look at it. The literary/linguistic evidence paints a picture of very advanced societies while the archeological evidence paints a distinctly different but again advanced societies.
Hence studies like the OP's submission are very much needed and welcome.