Claremont started the trend that all the other writers would continue when it comes to the Phoenix and that is to define it in a variety of ways including sometimes within one story. There are many contradictions when it comes to the Phoenix let alone the Jean/Phoenix connection.
Hopefully Gillen's story helps and not hurts but at this point I don't know if they could do anymore damage - the damage is done and quite extensive at this point. I just assume the Phoenix is too complex for our human minds to understand (I'm teasing lol but I do hope they can reign in some of the craziness from the last few years and define the Phoenix in a better way).