That is in fact the point of the lesson ... because Barack Obama by his own admission had British citizenship at birth that his father registered for him, Barack Obama could not be an American citizen naturalized until his British citizenship expired. You tell me the U.S. has never recognized dual citizenship (false, I have a cousin who is now naturalized here and still holds her Mexican citizenship) yet you expect that Barack Obama can claim British and American citizenship? Is that what you’re trying to tell me?
Look at it this way - if Britain enacted a law stating that any person who has at least one British grandparent is a British citizen, would that mean that the grandchild of a British citizen, born in the U.S. to U.S. citizen parents would not be a "natural born citizen"? After all, under British law, that child would be a British citizen.
The point, of course, is this: It is absurd (and in fact dangerous) to think that an American's citizenship - or eligibility to be President - can depend on the operation of foreign law. I do not want any foreign country to have any say, even incidentally, over who can or cannot be my President.
But a parent cannot refuse citizenship for his minor child, so Obama would still be an American citizen by birth to an American citizen - his mother.