He still has a specific date and place of birth. Usually those details need to be removed when the parents are removed, because they come from a baptism, which obviously links with the parents. If they aren't the parents, the baptism is somebody else's. One of my pet hates is when people snip off "unsourced" parents and leave the baptism behind.
However, in this case, it seems those details didn't fit with the parents removed. I guess they're probably a hangover from a different theory about his parentage.
Sometimes, with an immigrant of unknown origin, you have an age at death or when making a deposition, so you have an approximate birth year that definitely relates to the right person. But it's unusual to have an actual date or place of birth in the American evidence.