Given it's a drama based on real events rather than a faithful documentary, I personally think the music works quite well, if anything it serves to remind the viewer that some aspects have been embellished.
I wonder whether music louder than the dialogue is a modern thing; I ridicule my daughter for watching films with the subtitles on (she has no hearing issues) but ended up doing it myself for this one and was surprised to find it improved my enjoyment. Won't tell the daughter though!