That depends very much on the kind of aircraft, and while there are aircraft for which this is true this definitely isn't always the case. Modern aircraft are miracles of efficiency.
Most fuel is used to haul the airframe, cargo and the passengers around, fuel is only a relatively small percentage of the total maximum take off weight.
For example, the A350 mentioned in the article has a maximum of 108 Tonnes (140K liters) of fuel on board and has a maximum take-off weight of 280 Tonnes. So no matter what the mix cargo/passengers/fuel is there will never be more than 30-40% of the take-off weight in the fuel, and a good chunk of that (5 - 7 Tonnes) will be burned just on take-off and another 5-7 Tonnes to get it to altitude. So fully 10-14% of the fuel will be gone after the first few minutes of flight, then once you reach cruising altitude the consumption drops quite a bit due to the reduced drag.
Consumption during take off and getting to altitude varies between about 2.5 and 1.0 times consumption at cruise altitude due to increased drag and the climb itself.
With that kind of penalty on a take-off and the required reserve on landing (which is usually dead weight, but which you will very much appreciate if you have to get to your first or second alternate) the overhead of a landing+take-off sequence is pretty stiff so non-stop flights have a good chance of being more efficient if the destination is in range.
You are completely ignoring the cost of cycling an aircraft, and that pretty graph is less than 10% spread from min to max efficiency. So no, you will not be better off landing.
Maximum efficiency merely indicates at which distance all parameters are matched most perfectly, it is not the distance above which one should land to take on more fuel to be more efficient.
Reduction to absurds is an easy way to prove that to yourself, imagine a flight of 3000 miles at maximum efficiency, and then one at 3001 miles at which you claim they should stop to take on more fuel. This clearly is not the case so there is something wrong with your statement.
Just to nitpick a little: The peak efficiency seems to be around 2500nm, and it's pretty flat between 2000 and 3000. Above 2500 nm, you have to compare to distance/2, since you compare between 1 and 2 legs. Example: compare the efficiency at 3000nm and 2*1500nm. The cutoff is slightly higher than 2500nm. But not far from 3000nm. Coincidentally London-NYC is 3000nm. So anything longer than that could be split off (if you don't take a detour to do so).
