In a nutshell:
Jamelle Bouie, who finds the ad misleading, acknowledges its power:
In this narrative, the GOP didn’t mismanage the economy into the deepest downturn since the Great Depression. Rather, the economic crisis simply happened, ex nihilo, and Obama did nothing to stop or mitigate it. What’s more, he made things worse, with government spending and an explosion of debt.
And this really was an Etch-A-Sketch moment for the GOP. After Obama's first budget, the Republican right immediately blamed all the pre-existing debt and all the future debt on the president in office barely a month. They don't want a narrative. They require amnesia.
But exploiting public discontent by simply blaming the dude in power is effective, if crude, politics.