Apparently they aren't true. Read on for the details from Mr. Michael Ausiello at TVGuide.com:

Maybe it's the show's impending post-strike return. Maybe it's the success of that mediocre movie with the dresses. Or maybe it's that recent National Enquirer story. Whatever the reason, rumors that Katherine Heigl's Grey's days are numbered have staged a Hillary-type resurgence this week. But does the prattle have any basis in reality? A well-placed Seattle Grace insider, who, it should be noted, has never steered me wrong before, insists that Heigl remains "under contract" and adds that there are "no plans or discussions" for her to exit the series. End of story. At least until the end of her next contract cycle. Of course, Heigl wanting to leave Grey's and actually leaving Grey's are two very different things. That's not to suggest she wants to leave. Just that the two things are different. I want to be very clear about that. All this talk about Heigl not leaving Grey's has me wondering: Could the show survive without Izzie? Gizzie, yes. But Izzie? Thoughts below please.