You are forgetting that the individual might consider the gender to be private information. Some people might want to use a different gender in different contexts. See the ESPN/Grantland suicide issue recently if you care/dare.
A person using the name "Jack" is unlikely to be assumed to be a woman, even if that person selected "female" from a drop down somewhere. If the same person uses Jack/M and Cindy/F in different contexts, no fuzzy algorithm is going to resolve them as the same person (bar some other, stronger ID, such as a SSN).
EDIT: I initially used "William" as an example. Ironically, it turns out that name is only 57.6% male. Both Jack and Cindy are 90% male/female.
You have just used the numbers from the API as evidence of its own accuracy.