Personally, yes, I do believe this is the source of the “Kenyan birth certificate.”
First, the Kenyan one LOOKS like a fake when you look at it really close up. This one doesn’t.
Second, it has obvious markers of being a fake. For one, the fact that the “Republic of Kenya” did not yet exist.
For another, the blurriness of the “seal.”
Third, the fact that the book and page are IDENTICAL, and that both the Registrar and the District Registrar are virtually so (different only in their first initials) is way, way too much to be coincidence.