So, he never admits that Junior is his son, but he invites Junior's pregnant mother to take a trip half way around the globe where she meets with his family and gives birth?
What part of that seems logical or makes sense? Why would she travel anywhere with a man who wouldn't admit he was her child's father?
If what you say is true, why would she go to Kenya?
She very well could have traveled there in her attempt to "create" this background for Jr.
At this point, it's not 100% confirmed Sr. is Jr.'s biological father. In fact, there's only Barry's word. Do you trust Barry's word? I don't. Therefore, IMO, this is at least a possibility.