This is not true as far as the perception of the human eye, since the eye's response to PWM is extremely non-linear. From direct experience, I have found that if you want 8 relativly even steps of intensity you can use duty cycles of:

7: 100.0% (brightest)
6:  50.0%
5:  25.0%
4:  12.5%
3:   6.3%
2:   3.1%
1:   1.7%
0:   0.0% (off)

So you see that using a 1/8 duty cycle still provides in excess of 50% perceived brightness.

However, don't expect that doubling the current will get the 1/8 duty back to "full" perceived brightness, because the output of the LEDs wrt current is also non-linear.