It's not inaccurate. It's just not accurate either.
Fiscal 2009, Obama's first year in office, was Bush's last budget and was also the largest deficit in American history for one reason: the one-time costs associated with TARP. It was more than three times larger than FY2008. Obama's first three budget years ('10, '11, '12) did NOT have one time costs associated with TARP but are still the next three largest budget deficits on record, which is to say they "shrank" by comparison to '09, but were still ridiculous. In the end, all but 1 of Obama's budgets produced deficits larger than any of Bush's non-TARP budgets.