What could be an explanation that the outer jacket of the cable could affect the audio quality?
The outer jacket lies outside the shielding layer, so no effect could be expected from this.
(This reminds me a bit of people buying an expensive cable between their CD player and the amplifier; low output impedance, high input impedance, resistance and capacitance of the cable are negligible. And yet people who buy a $100+ cable, now called an 'interlink', -sounds more impressive-, say: "it sounds better now". I suppose they want to hear the money that is no longer in their wallet...)