You seem to be overlooking the fact that facts involving contextual language are facts nonetheless.

The "fact" that Obama is president is only social truth. Obama is president because we decided he is. If no one >thought Obama was president, he wouldn't be president anymore.

There is a counterfactual sense in which this holds some weight. I'm not saying agree with your claim, but I would at least have to give it more consideration before I knew what to conclude.

But that simply isn't the case (& it's a fact that it isn't, of course). Obama's (present) presidency is not contested, and it is a fact that he is President of the United States.

You could try to argue against admitting facts involving any vagueness of language, but you would run into two problems: this is more an issue with language than an issue with facts; and you have already admitted facts about other things.