The quoted statement says "energy to move a kilometer".
On an "energy to move a kilometer" basis, the statement is definitely false.
Acccording to Dr. Karen Oberhauser, a tagged monarch butterfly has been confirmed to travel 265 miles in one day.
According to How Much Fuel Do Monarchs Burn? reporting Dr. David Gibo's research:
On 140 milligrams of fat a monarch butterfly has enough energy to continuously flap its wing flying for 44 hours and to soar or glide for 1040 hours!
So the butterfly is using at most 3 milligrams per hour.
For comparative human statistics, use this excercise calorie calculator
For a 110 pound (50kg) human:
bicycling 16-20 miles per hour 599 dietary calories (kilocalories) are used per hour. This corresponds to 67 grams (67,000 milligrams) fat per hour.
bicycling at an unspecific "greater than 20 mph" racing speed is 798 calories per hour.
This corresponds to 89 grams (89,000 milligrams) fat per hour.
Humans use more than 1000 times as much energy per kilometer as monarch butterflies, even considering the record distance on a bicycle for a day is 521 miles, about twice the butterfly's record.
Note: although the quoted statement clearly says "energy to move a kilometer", and nowhere suggests that mass moved should be considered, another way to consider efficiency is
(energy used)/((mass of organism)(distance traveled))
On this basis, swimming animals have been found to be the most efficient animals.
All credit to Brad J. Gemmell, Passive energy recapture in jellyfish contributes to propulsive advantage over other metazoans Proceedings of the National Academy of Sciences of the USA volume 110 pages 17904–17909.
As reported in Eel migration to the Sargasso: remarkably high swimming efficiency and low energy costs, the eel is very efficient.
Particularly, its efficiency is calculated to be 0.5 kilojoules/kilometer/kg.
Let's compare this to a human bicycling.
I'll use a 50 kg human, 29 kph (18 mph), 599 kilocalories per hour.
599 kilocalories/hr is 2500 kilojoules/hr.
This corresponds to 86 kilojoules/kilometer.
Or 1.7 kilojoules/kilometer/kg
Eel is more efficient by a factor of 3.
(From the jellyfish article it can also been seen that a species of jellyfish has about the same efficiency of the eel. Large marine animals such as whales do not seem to have been considered.)
See also Swimming speed, respiration rate, and estimated cost of transport in adult killer whales, which shows that at an optimal speed of around 3 meters/second, killer whales have an efficiency of 0.78 kilojoules/kilometer/kg. Better than a human on a bicycle, but not quite as good as an eel.
According to Energy in Nature and Society: General Energetics of Complex Systems by Vaclav Smil, at page 103
for a 15-t gray whale is 0.4 J/m kg (if this exponent holds than a baleen whale would need [less than] 0.1 J/m kg)
See also Comparative analyses of animal-tracking data reveal
ecological significance of endothermy in fishes which shows some sharks have efficiency in the 0.1-0.2 J/m kg range.
In conclusion, a human on a bicycle is NOT the most efficient. Whether the quote is analyzed literally on an "energy to move a kilometer" basis, or alternatively as energy per distance per mass of organism, there are more efficient species.