If the wires for the LED cluster are in the same cable it is not just airborne EMI but capacitive coupling between wires in the cable that is the problem… Good Design would dictate that power and signal wires should be separated or shielded when they are in the same cable. Many manufacturers make cable with both power and signals in the same cable (used in motor control applications and the like) and the signal wires are usually individually (each pair) foil shielded with a bare wire stringer included for grounding. The pairs are usually also twisted pairs, which also helps with cross coupling. See example Belden wire 3086A.

The shielding will also cut down on airborne EMI.
A decoupling capacitor (anywhere between 0.1uF to 100uF depending on what will be required ) used on the output of the power supply and/or the lamp housing should also help with eliminating the coupling problem.

In the application they are talking about they don’t mention the current involved with each of the applications and it is the current involved along with the frequency that generates the level of EMI.

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