We don't get the History Channel where I live, therefore our history remains intact 

So the photo in question is now believed to have been taken 2 years before they would have been flying in that area?  Well, it is the History Channel, so perhaps the next chapter in this story will be that the photo is genuine and was actually taken in 1937, but the ancient aliens came back, stole that photo, then traveled back in time to 1935 to have it published just to throw more mystery on the disappearance of Earhart and Noonan.  And the real reason Earhart and Noonan disappeared?  Ancient aliens abducted them.

The mystery of Amelia Earhart was solved years ago. Everybody knows that Captain Janeway and the crew of the USS Voyager found her and Fred Noonan on an alien planet seventy thousand light years from Earth.

The way things are going with technology, there will eventually be a good high resolution scan of the sea bed at 17,000 ft. depth, on a direct line from Lae Airfield to Howland Island. If the plane didn't break up on contact with the water, there should still be enough left to identify it. 

This is just one of those "tech isn't good enough yet" things, like figuring out where the much more recent Malaysia Airlines Flight 370 ended up. We're just not very good at sea floor searches in very deep water yet, unless it's something huge and with a well-established location like the Titanic.