The major flaw is, as you guys pointed out, the one in the lake. And also he says "there are 13 of these stones throughout the land" and every stone gives 30% skill increase to Combat/Magic/Stealth skills. It seems unlikely that Bethesda would have devided the 13 birthsigns up into these catagories.
Just recounted; I see 24 X's on the map. There are 13 birthsigns. Maybe that was what he meant.
Note that in the video, there were three stones, belonging to the guardian signs, in one location. Maybe those same three can be found in other locations as well, with stones for the other 10 birthsigns scattered about as well. As for the one in the lake, maybe it was built before there
was a lake there. Perhaps the Reach canyon was created by two tectonic plates drifting apart, which created a sinkhole that became the lake -- and the stones are
really ancient. Just a thought.