So is the example in this video impossible LINK ?Schematic came up as I was typing - yes, the green wire short circuits the LEDs so they should not / cannot light.
If the green wire is connecting the bottom end of the resistor where it joins to the LEDs to "ground" (negative side of the power supply), it should prevent the LEDs from lighting - it short circuits them. They may have lit with the 10 ohm resistor simply because there is enough resistance in the green wire to allow enough voltage to light them.
Those clip leads are notorious for being high resistance from the start and getting worse as they are used and strands in the wires break, at least in my experience. I used to buy cheap clip leads. With the better quality ones I'd just replace the wire with 22 AWG wire properly soldered to the clips. With the really cheap ones, I'd keep the insulators for the clips and scrap both the clips and the wire.

