The reasons why they believe these things are also different - I haven't read Fomenko, but the videos above seem to focus on a belief that oldish-looking buildings can't be relatively new (they know this becaude they can't find examples of large oldish-looking buildings being built literally today in their area) , so they must have all been dug up from a much more advanced prior civilization, after they had been buried by the flood of Noah.
As I said, I still doubt some of the explanations brought forward (e.g. the mining activities in the video I just mentioned) but when you see so much visible stuff from satellite imagery in the middle of nowhere in North America it really makes you wonder what was there, what do our history books say?