IF you believe her premise that she really thought, for whatever mitigating reason, exhaustion, drunk, stoned, enraged not due to the decedent etc, she was at her home and believe she really thought he was an intruder....then no, it isn't murder, it is manslaughter despite the fact that at the point she "believed" she thought it was her home, she did shoot with intent to kill.
The reckless element of manslaughter means she was reckless in assessing the situation she created or found herself in and if substance impaired; it is still at least manslaughter.
You try driving like hell on wheels sufficient to get pulled over for reckless driving. See if you talk your way out of it by pleading you were simply tired. Probably won't happen especially if you are going fast enough to make the reckless offense bookable.
Murder would mean you do not believe her stories about truly believing she was at her apartment.
Me personally, I don't believe anything she has to say, not for a second.