The NEHGR article is on the NEHGS website at http://www.americanancestors.org/databases/new-england-historical-and-genealogical-register/image/?pageName=134&volumeId=11728&filterQuery=databasename:new%20england
The author obtained microfiche of the church record from Hingham, England, where Ann's 1628 marriage to Stephen Gates was recorded. Her last name in the record of the marriage had previously been read as "Veare," but the author explains how the interpretation of the handwriting could be ambiguous. He says the first letter resembles both the V in "Vincent" in another record from 1628 and the N in "November" in a record from November 1627. Comparing the fourth letter to the letter "r" in the words "married" and "buried" and the letter "v" in "November" in records on the same pages, he states that the fourth letter in the name is clearly a "v" and not an "r".
Additionally, he explains that most marriages took place in the bride's home parish, and because another researcher had determined that Stephen probably did not reside in Hingham parish, it's even more likely that Hingham was Ann's home parish. He looked for the names Veare and Neave in various Hingham parish records and found no other occurrences of the name Veare, but 31 occurrences of the name Neave (plus 3 others that could be either Neave or Neale).
The analysis of the handwriting and the absence of other records for people named Veare and the abundance of records with the name Neave are strong evidence that Ann was a Neave and not a Veare. I find this evidence convincing.
The article states that the marriage record is on FHL microfilm 1,526,135.