The RNC convention is decorated by banners that say "We Built It." It. Not "that." Obama said "that." Even when attempting to deliberately misinterpret his sentiment, they can't help but tacitly admitting that "you didn't build your business" isn't what Obama was saying by correcting the grammar for their jeering slogans. Had Obama meant "you didn't build your business" he would have said "You didn't build it."
"That" can only refer to something else. Grammatically, it can't refer to the business mentioned in the first part of the sentence. If the banners said "We Built That" everyone would look at it and say "Built what?" When changed to "We Built It" one knows they mean "we built the businesses that we're mendaciously claiming Obama said you didn't build." To wit, It and That are not synonyms.
I know it's ridiculous to have to provide basic lessons in the English language to a political movement that to a person almost exclusively speaks English as a first language, but that's a great example of just how monumentally stupid they think that their own supporters are, and voters in general. (Did that last sentence just read weird? I should have said "but it's a great example of just how..." See? Not synonymous). The disingenuous outrage over Kerry's botched joke in 2006 was somehow more plausible than this.