I saw this too...I'm hoping Robert99 will weigh in. The Marshall Islands would be quite a long away off course -- unless the plane was found floating and towed to the Marshall Islands. If this photo was date stamped July 1937, that would really make it interesting.
There is a special this weekend about this (I think maybe on the History Channel), so I'll be curious what they say.
Whatever it is on the barge behind that large ship is not a twin engine airplane of even a part of one. At most, based on the "fuselage" appearance, it would be a single engine plane, assuming it is an airplane in the first place.
I personally can't tell for sure if the "woman" who is suppose to be Amelia is even a woman. And I would suggest taking a further look at Noonan's hairline before concluding that it is Noonan in the picture. If that is Earhart and Noonan, it looks like they are perfectly free to go to a telephone and call home.
There were plenty of Europeans in the Southwest Pacific in the 1930s so, in my opinion, the picture doesn't mean anything with respect to Earhart and Noonan.
There is nothing, repeat nothing, to even suggest that Earhart and Noonan were headed anyplace except Howland Island. The Gardner Island theory would require another three hours of flying from the point where Earhart told the Itasca at Howland Island that "we must be upon you", and would require another non-radio procedure, such as they were obviously using at Howland, to locate Gardner Island.
In my opinion, if they had another three hours worth of fuel at the above time, they would have been able to get their navigational problems corrected and landed at Howland.
So the above puts me in the "crash and sink" group that believes Earhart and Noonan ended up in the water near Howland Island. And there I firmly remain. 
Robert -- is it also you're opinion that even if they ended up in the water somewhere with empty fuel tanks, the plane would not have floated? I read initial reports believed the plane would float, but I also read others that said they would not.
Mark,
Let me do something and I am relying on numbers from memory here.
The aircraft had several fuel tanks with the total fuel capacity being 1100 gallons. When they took off from Lae, a 100 gallon fuel tank only had 50 gallons of 100 octane fuel in it. In 1937, 100 octane fuel was just coming into use and not readily available, especially in remote locations like Lae. The 100 octane fuel was developed to prevent engine detonations during full power operations such as take off. After the 50 gallons of 100 octane fuel had been consumed, certainly within the first 45 minutes or less after take off, only 80 octane fuel was available for the rest of the flight to Howland. I believe they had several 55 gallon drums of 100 octane fuel waiting for them with the Howland party.
The fuel tanks have to be vented so that air can enter the tanks as the fuel is burned off to prevent vacuum locks that would prevent the flow of fuel. Typically, the air vents (and there may be several) start at the highest point in the fuel tank system, go up even more to ensure that the vents are always above the tanks, and then extends downward below the bottom of the fuel tank system. Thus the air entering the tanks start below the tanks and any fuel that gets into the air vents will drain out below the tanks. You could presumably turn this tankage system upside down and only lose a small amount of fuel from the system, which is a safety factor to the extent that it prevents fuel draining into the aircraft cabin or being lost overboard.
Anyway, on take off from Lae, Earhart and Noonan had 1050 gallons of gasoline on board with a total weight (using 6 pounds per gallon) of 6300 pounds. The total fuel tankage could hold 6600 pounds of fuel. Salt water (sea water) weighs 8 pounds per gallon. Consequently, the total tankage could hold 8800 pounds of salt water. Or to put it another way, when filled only with air the total tankage had the capability of providing 8800 pounds of flotation capability in salt water. This is roughly the same as the zero-fuel weight of the aircraft.
Assume that the aircraft was able to ditch without doing any damage to the fuel tankage system, the wings and fuselage are not sealed and salt water would get into them. Additionally, from what I have seen over the years, ditched aircraft tend to take up a nose underwater attitude soon after entering the water. This change in attitude would almost certainly expedite getting the tanks air vents underwater and slowly but surely filling the tanks with sea water. There is really no way to prevent that.
So to make a long story short, the Electra would probably be able to float for a period of time, maybe several hours, but it is going to sink sooner rather than later. The sinking point is reached when the flotation capability of the fuel tanks is less than the combined weight of the aircraft structure and the sea water that is in the fuel tanks.
