This is 100% incorrect.
Driving an LED at lower currents results in a higher efficiency, lm/W.
So 10 LEDs running at 1W each will produce more lumens than 1 LED running at 10W, OR 1 LED producing X lumens will use more power than 10 LEDs producing the same amount of lumens combined.
The higher efficiency also results in less heat being produced.
Just to dot the 'i's and cross the 't's, you only get this improvement if you compare 1 LED vs multiples
of the same LED. Ten 1W LEDs running at 1W each would be about the same (generally) as one 10W LED running at 10W, while ten 10W LEDs running at 1W each would produce more light and less heat. It's an expensive way to gain efficacy.
...(author thinks a bit)... ...just how much efficacy?...
It's not a small difference! I just did some estimates from the XM-L2 datasheet (granted it's getting a bit long in the tooth, but it should be at least roughly representative). Running one 5000K T5 bin at 3A, 85C, you'd expect 845lm. Running ten of those at 300 mA, 85C you'd expect around 1300 lm. If you took advantage of the numbers to spread them out and dissipate the heat better, keeping them at 50C junction temp, you might get closer to 1430 lm, an impressive 69% increase.
Also, this is at 1/10th the current, not 1/10th the power. Because of the lower Vf at low current, the actual input power would be about 17% less, making the overall efficacy just over double.
This is certainly not the result I expected!
Hmm, what if we only used two LEDs?
one LED, 3000 mA, 85C, 845 lm, 3.3V, 9.9W, 85 lm/W
two LEDs, 1500 mA, 85C, 936 lm, 3.05V, 9.15W, 102 lm/W
two LEDs, 1500 mA, 65C, 983 lm, 3.05V, 9.15W, 107 lm/W
ten LEDs, 300 mA, 85C, 1300 lm, 2.75V, 8.25W, 158 lm/W
ten LEDs, 300 mA, 50C, 1430 lm, 2.75V, 8.25W, 173 lm/W