If Obama was going to release the originals, then you are right. However, he released something that looks to me like what Hawaii issues now - not the original document, but a document with information placed into it.
It looks like a computer-generated paper form. If I ask Minnesota for my birth certificate, I now get one similar to that - an ‘official form’, but not the original documents. And I would assume it would be pretty easy for the head of a state agency, with lots of democrat workers, to produce a state document pretending to have real info in it.
That seems a more plausible route for forgery than digitally altering an image.