I'm only answering because no one else has since I am no expert. Recently, there was another post (by someone who is more of an expert) about DNA matches and he indicated that a DNA match of 3 generations or less is helpful. I think the 3xGGF is too far away, so that you will need more DNA matches to triangulate to be sure that it is a true match.
The birth date can be problematic. Where did you find the two birthdates? Is one a birth or baptismal record? Is it from the census? You need to consider how the information was obtained. If it is a census record, it is hard to take that information as 100% accurate. The information could have been provided by a neighbor or grandpa who doesn't really know everyone's birthdate. The reason I say the birth date discrepancy is a problem is because, in my own family, my grandfather's children were MaryAnn, Salvatore, Jack, and Joan. His brother's children were Salvatore, Jack, MaryAnn and John. Salvatore from one family and Jack from the other were born on the exact same day, year and everything! So confusing. So, you could have a situation similar to this.