Don't see it that way myself, GoMotor, because, as mentioned, the signal LEDs remain, "polarized," they send juice only one way, and will not function as conduits for both left and right turn indication.
A riding partner has LED signal lights, without the diode-and-ground mod I mentioned for his incandescent indicator light. Right turns, the indicator is activated. Left turns, although the signal lights flash, no indicator light from the incandescent bulb. The incandescent bulb is non-polarized. Don't see how a non-polarized LED (a regular LED with a half-wave or full-wave rectifier) would behave differently.
The mod, by contrast, provides a fixed ground for one connection of the indicator bulb. With the diode/rectifier connection to the other indicator bulb connection, ANY positive voltage cycle will light the lamp. If the non-polarized LED enjoys a fixed ground, it would flash on both left and right turns. Connected as the stock non-polarized incandescent indicator light bulb, I don't think so.
That said, I may be in error; apologies/regrets in advance!
No apologies/regrets required. We are just searching for enlightenment here. I can tell you that I have a non-polarized LED indicator with incandescent signals and it works properly. I have put a polarized indicator bulb in and it only worked in one direction and if flipped 180 degrees it only worked in the other direction. With the two diode mod a non-polarized LED could be made to work in both directions.
I could make a system behave like your friend's by grounding the indicator bulb wire that should go to the left side.
We agree that polarized LED signals pass current only one way to ground, but that is all that is needed for a an incandescent or a non-polarized LED indicator to work without the two diode mod. I can't think of a better explanation for this than this paragraph from post #8 above:
When the switch sends sends positive voltage to the signals on one side for a turn that same positive voltage feeds through the indicator bulb and goes to ground through the element in the off side signal lights. The dash indicator passes so little current that the off side signals do not light up, but the current flow is always from positive to ground through the signals on both the on side and the off side. LED signals would behave the same way with current always going only one way to ground on both the on side and the off side.
The current is always going only one way to ground through the signals (incandescent or LED) on both the turn side and the off side no matter the type of indicator bulb.
There is still the question of how much current flows through the off side and will it light the indicator properly or cause the off side signals to glow. The two diode mode will eliminate that question.
By the way, I am guessing that the small non-polarized LED bulbs just use two separate parallel internal LEDs in parallel with one wired +- and the other -+, but that is just a guess.