Native of is not to be used as birth place according to the field help. An example: I would be considered a native of South Dakota as I have lived here all my life but I was born in Minnesota.
Native is related to the word natal. In Spanish documents where "nativo" is used the meaning, if perhaps not strictly enforced, is that the person in question was born there, as opposed to "vecino": resident (literally "neighbor") of a place.
It depends on the project, but, in general, Native Of is not considered the birth place. However, there have been projects where the instructions specifically tell you to use Native as the birthplace. That is another reason why the field helps are so important.
By definition it means born there, and on forms that say Nativity or Native Of, that's what they mean. However we're to follow the project instructions for this project and disregard the meaning if it says not to use it as a place of birth.
If the project is US, Pennsylvania, Western District—Naturalizations, 1820–1930 [Part A], look at the samples in the project instructions. The field help, unfortunately, doesn't clarify here.
When a birthplace is listed, it is indexed. Sample 1
But when "a native of" is used, it is not indexed. Sample 2