Yes, the crash began before Obama was sworn into office. And yes, Bush did administer the beginning parts of TARP. And yes, that certainly had an effect on things. The Fed's actions came into play as well.
But my point, which I could have stated more clearly, was that the market bottomed out shortly after Obama was sworn in. And you can see that after the stimulus, the market began to recover.
That's not to say that the stimulus was solely responsible for the recovery. I'd wager the Fed's role had the greatest total impact on the economy. But it did have a significant effect.