You were doing okay until you got to this point.
If your wife has a child and you aren't the father it doesn't mean she didn't have a child.
If you have another, legitimate wife somewhere else, and have a child with a woman who thinks she's married to you, it's not the other woman's (true legitmate wife's) child.
Sorry if these examples are too personal, but what's involved are different levels of reality -- the legal and the actual or physical.
You can have a child in an illegitimate or fraudulent relationship, and that doesn't mean that the child is actually from your legitimate or legal relationship.
Maybe that's not what you're getting at, but as crazy as the idea that Stanley Ann and Barack Sr. flew off to Kenya to have a baby is, the notion that they tried to pass off Barack's child with Kezia as their own is even loonier.
I have seen several posts that state that Obama Sr. and Ann Dunham were never married--No one has been able to produce a copy of their marriage license, public announcement, or even divorce records.
If they weren't married, then the "Mr and Mrs" birth announcement was fraudulent. The only way it could be "true" would be if it were referring to another Mr. and Mrs. Obama--hence the conjecture, which is admittedly way out there.