Claire kills Justin with the axe, Jin tells her Kate has Aaron

Back with crazy Claire, she is holding the axe and threatening Justin and asking where Aaron is. Justin repeatedly tells her that he doesn't know and that they don't have her. She's obviously been convinced by Christian and Locke that they have Aaron.

So she starts to swing the axe at Justin when Jin tells her to stop. Claire says that the other stuck her with needles and branded her, just like they did to Sayid. She shows Jin the scar from the brand. As Claire prepares to swing again, Jin tells her that Kate took Aaron off of the island. Justin tells her that Jin is telling the truth and pleads for her to let him go. Claire pauses for a moment and then swiftly buries the axe in Justin's chest. Jin is stunned.

So why did Claire kill Justin even though Jin told her the others didn't have Aaron? Did she think Jin was lying or was she going to kill Justin no matter what happened?