No. It's simply a constitutional issue.

You have to abide by ALL the provisions of the constitution. If they can set this glaring precedent (have a non-citizen serve as president), then what's to stop the scrapping of the rest of the document?

As a UK outsider, I can't see why you did not ask any of the 'origin' questions about preceding Presidents that you are asking about this one. Were you personally demanding to see the birth certificiates of both Bushes? Nixon's? Truman? And it's a modern world - maybe we should really be carrying out DNA tests as well to make sure the people named on the certificate are actually the parents ...

So I see no reason for the different behaviour. Apart from the one glaringly obvious reason that you would deny, of course.