Short of possessing omniscience (nope) or a perfect historical record (which, by definition, never exists) the "it's possible" scenario in historical accounts often can't be excluded. Though it's still an Occam's Razor world I inhabit, and so the "is it plausible?" question persists.
Under your Dr. Sinclair hypothesis, did Sinclair actually attend a birth? If so, I see no reason at all for him to think any of the information supplied was false. If not, why on earth would a physician potentially put his medical license on the line to help out some African dude (whom he's likely never met) or even to help out the Dunhams (who had just moved to Hawaii about a year prior; it's not like he's been their trusted family physician for generations)?
And what might have been falsified?
BHO as father? That seems doubtful unless one wants to do the "does the Prez look more like F. Davis, Malcolm, or the Subud guy?" bit. Once that INS gambit failed and BHO returned to Africa, why maintain the pretense that BHO was Obama's father (to the point of letting Obama publish an entire book about this) if he was in fact not?
Stanley Ann as mother? Even less likely. A family foisting off someone else's child onto their 17 year old daughter, who nonetheless maintains a lifelong relationship with Obama? Nah.
Obama not being born in the U.S.? Again, the alternatives are less plausible than the story told by the birth certificate. Kenya can near absolutely be precluded given the timetable of when the Dunhams arrived in Hawaii and when S.A. was back in Seattle, plus the records which show only 1 person coming from that whole region of Africa to the U.S. in that time period (S.A. plus baby makes two.) Washington? Obama is still a U.S. citizen; why forge the birth in Hawaii? Canada? An hypothesis lacking even a shred of direct evidence.
A falsified-from-the-start certificate is possible, but at the end of the day, not very plausible, no mater how one slices this.
Your opinion really is not worth the trouble to read.