So when I wanted the epic pirate music for my planets, I noticed that some factions lacked a music section in the .faction file. Those get the 'default' music tracks. The filename-to-string mapping is done in sounds.json, and that contains the names for the default tracks.
And that's why Independents, Persean League and the player faction have the same music: they all lack music sections in their faction files. A faction without a music selection would be the equivalent of having this in the .faction file:
"music":{
"theme":"music_default_market_neutral",
"market_neutral":"music_default_market_neutral",
"market_hostile":"music_default_market_hostile",
"market_friendly":"music_default_market_friendly",
"encounter_neutral":"music_default_encounter_neutral",
"encounter_hostile":"music_default_encounter_hostile",
"encounter_friendly":"music_default_encounter_friendly",
},
In my case, I just wanted the pirate music, so I added this to player.faction:
"music":{
"market_friendly":"music_pirates_market_friendly",
},