In season 1 episode 13 of the rebooted Doctor Who, The Parting of the Ways, Rose Tyler looks into the Heart of the Tardis and...
becomes the Bad Wolf entity.
This makes her effectively a Goddess, with the power to transcend space and time scattering messages through it, and destroy things by dividing their very atoms. In this question, it's made clear that a Doctor possessed in the same way would be far more powerful a creature:
Doctor: [Rose] came back. Opened the heart of the Tardis and absorbed the time vortex itself.
Jack: What does that mean, exactly?
Doctor: No one's ever meant to have that power. If a Time Lord did that, he'd become a god. A vengeful god. But she was human.
Doctor: Everything she did was so human. She brought you back to life but she couldn't control it.
Doctor Who Series 3 Episode 11: "Utopia"
This quote and the answer it comes from seems to imply the Doctor has never been possessed by the Space-Time Vortex, although this is untrue.
Minutes after Rose creates the Bad Wolf entity by looking into the Heart of the Tardis, the Doctor saves her by kissing her in order to absorb the Vortex himself - an act which would go on to destroy his current incarnation - before channelling it back into the Tardis. For this brief moment, the Doctor possessed all the power of the Vortex inside of him, even though the quote from the Tenth Doctor in Utopia claims this has never happened.
Why does the Tenth Doctor claim that something like this has never happened?
When it did happen, why wasn't the Ninth Doctor transformed into the God-like, vengeful entity that the Tenth Doctor claims? Why was he able to simply control its urge and pass it through himself?