Residents say the woman had psychiatric problems and had been involved in a dispute with a neighbor, a fireman over loud music, during which she threatened to set fire to the building.

【翻译】当地居民说，这名女子有精神问题，曾与一名是消防员的邻居因喧闹音乐而发生争执，在此期间，她威胁要放火焚烧大楼。

网友的理解完全正确。

a neighbor, a fireman：中间没有and 连接，说明是同位关系。指同一个人，即“同位语”，“这位邻居是一位消防员”。