I had to test the "myth":
I have a clock module with a 4-digit 7-segment display. I tested two methods: 1) Turn on all segments in each digit and multiplex the digits and 2) Turn on each segment and multiplex the segments and digits (turn on seg a, digit 1...seg g, digit 1...segment a, digit 4...segment g, digit 4). I had it switch between the two methods and could not see any difference in brightness, and no flickering.
Using my Korad KA3005P power supply set to 5V it showed 23mA with method 1 and 21mA with method 2. Not a huge difference, but not nothing either. And messing with the duty cycle and refresh rate could bring both of those numbers down.