In the movie X-Men: The Last Stand (2006) Phoenix had the ability to scatter atoms of everyone around with a use of kinetic energy. Did Wolverine manage to come close enough to Phoenix because his healing factor was faster then Phoenix's destruction force, or because Jean's mind helped to strangle it for a short time let Wolverine come through?
I'm interested in the comic story line as well as the movie.
TL;DR : It was a combination of the two - Logan's healing factor + Jean's subconscious... but mostly Jean.
The scene in question, and in fact much of the plot for the movie, is loosely based on the original Dark Phoenix Saga that took place in The X-Men #129-138 waaaay back in 1980. At the end of that saga, Jean Grey
realized she couldn't control the Phoenix and committed suicide to stop it.
Within the context of the movie, however, it would seem that Jean was attempting to fight the Phoenix personality from within. Furthermore, she had previously asked Logan to kill her when she awoke in the Mansion:
JEAN: Where am I?
LOGAN: You're in the mansion. You need to tell me what happened to Scott. Jean, tell me > what happened to him.
JEAN: (remembering) Oh, God.
LOGAN: Look at me. Stay with me. Talk to me. (cups Jean's face) Look at me. Look at me.
JEAN: No.
LOGAN: Focus. Focus, Jean.
JEAN: Kill me.
LOGAN: What?
JEAN: Kill me before I kill someone else.
LOGAN: Don't say that.
JEAN: Please. (room shakes)
LOGAN: Stop it.
JEAN: (crying) Kill me.
LOGAN: Stop it. Look at me. Look at me. Jean. It'll be all right. We can help you. Hey. The professor can help. He can fix it.
JEAN: (reverts to Phoenix personality) I don't WANT to fix it.
Also, at several places throughout the film it would seem that the Jean personality was influencing the Phoenix personality, just enough to rein her in. It should also be noted that the Phoenix personality appeared to show a preference for Logan over Scott.
When Logan was attempting to reach Jean at the end, the Phoenix personality (or perhaps the Jean one) seemed almost impressed that he kept coming despite her attempts to stop him. Given her raw emotional state, the Phoenix personality probably found his persistence... invigorating. By the time he reached her, her thoughts most likely resembled the cover of a romance novel.
So it's entirely likely that one of the personalities - if not BOTH - allowed Logan to reach her on purpose, albeit for different reasons.
I haven't read the comic, but I have seen X-Men: The Last Stand multiple times.
In the climax of the film, we see Phoenix expelling energy/power in all directions while Wolverine walks towards her. This energy/power comes out in waves, as we can see when he is occasionally pushed back or forced to stand still when a larger "wave" hits him. As he continues to walk towards her, we see his skin begin to disintegrate, showing his bare skeleton (that is coated with Adamantium, a virtually indestructible metal) before his healing factor kicks in and begins to heal him.
Without both his healing factor and his Adamantium coated skeleton, he would be dead by now.
When he finally gets to her, the waves seem to subside for a moment and she tells him to kill her, her eyes changing from those of The Phoenix back into those of Jean Grey's. He obeys, and stabs her with his claws.
Although we have no canon answer thanks to the fact that we can't hear Jean Grey's thoughts, it is likely that Jean Grey was doing what she could to stop The Phoenix from killing Wolverine out right (hence the waves, rather than a continual output of consistent energy/power), and even then he only survived thanks to his healing factor and his Adamantium coated skeleton. When he finally reaches her, she manages to "break out" of being The Phoenix long enough to tell him to kill her, and more importantly, keep her powers controlled long enough to allow herself to be killed.
As such, it seems to be a combination of the two theories in the question that allowed Wolverine to kill Jean Grey.
