How can Obama make claims that directly contradict what 67 million Americans saw during the debate?

This is amazingly brazen.  From Fox News:

. . . At a rally Friday in Fairfax, Va., Obama claimed Romney had outright rejected his proposal to end tax breaks for oil and gas companies.  

"He said there's no way that he'd close the loophole that gives big oil companies billions each year in corporate warfare," Obama said, in the middle of a litany of complaints on Romney's tax positions from Wednesday's debate.  

Just one problem. Romney didn't say that.  

Rather, the Republican nominee said that if tax rates are lowered as his plan calls for, the $2.8 billion in breaks for oil companies should be on the table.  

Here's what Romney said:  

"But, you know, if we get that tax rate from 35 percent down to 25 percent, why that $2.8 billion is on the table. Of course it's on the table. That's probably not going to survive (if) you get that rate down to 25 percent."  . . .