Yes, exactly - a royal wedding is for friends and family, not a business/political thing at all. And even if it were, then yes, presidents and prime ministers from a whole host of countries would have had to be invited, rather than specifically just Obama. He is no more important than the others.
Good heavens, a quick google search reveals that America is actually seeing the Royal Wedding as a snub to Obama! Hahahaha! Check out the rumour that Snopes has cited: http://www.snopes.com/politics/obama/weddingsnub.asp