My personal opinion, which matters not to anyone but myself :) - LOL, is that the document was doctored in order for him to not been seen as the “son of a bitch” or “bastard” he actually is.
I have no doubt he can legally run for the office of POTUS, he just doesn’t want it known that his mother was a slut and his father a whoremonger. Nothing more, nothing less.
You may well be right.
“Oh what a tangled web we weave, when first we practice to deceive”...
Worth faking a birth certificate? Running for President? Nah.