did Clinton give away our National Parks to the United Nations
It isn't a lie, but it isn't what you are describing either. If you go a little further down in that clearly right-wing article you will see the statement "Biosphere Reserves and other U.N. designations don't give the U.N. formal authority to regulate American land."
What it does do is protect our national preserves no mater what party is in power. So if some Republican wants to drill for oil in a national park, it is possible that with enough political clout, they could push it through. It it is under United Nations protection, it would not be subject to the political whims of political parties.
It's a good idea in today's political climate and it protects our national treasures from those who would give into greed.