Several printed sources besides Cutter say this, but they don't describe the basis for believing it. John Parkhurst's wife is named Abigail in records, but Abigail is a common name, and the question is what tells us it is Abigail Garfield? Since there is never a precise marriage date, there does not appear to be any marriage record found. Abigail's alleged father died when she was unmarried, so his will does not prove this marriage. Is there a deed where John Parkhurst sells land inherited from his father-in-law? What is the basis for Cutter (or anybody else) to tell us John Parkhurst's wife was Abigail Garfield?
Anderson, as mentioned by a previous poster, says "probably", meaning he has no evidence to show it but has no better answer. However, his last paragraph hints at what I suspect to be the origin of this possible myth: a grandchild named Parkhurst in Edward Garfield's will, apparently assumed to be Abigail's before people realized that Edward's daughter Sarah married George Parkhurst. As near as I can tell, the marriage to John Parkhurst is now perpetuated merely because it always has been. But this was a ridiculous conclusion for people to reach in the first place, because the same will says Abigail is unmarried at the time.
Anderson cites Bond but Bond does not explain how it is known. And Bond is no improvement over Anderson, because unlike Anderson, neither Bond (nor Cutter) is the most reliable source. Worth believing if it is all you can find and have no problems, but not credible enough to believe when contradictions arise, unless primary sources can be found to confirm their information.
The problem that arises is the marriage of Joseph Gleason to Abigail Garfield. If the Abigail who married Joseph Gleason is not the daughter of Edward, there are some weird things going on, such as the proposed Abigail (Garfield) Gleason of unknown birth but estimated age 20 based on which family she would have to be from, marrying a man 20 years older than her, having no children, not being mentioned in her father's will, and being called "Old and crippled" when she would only be 50. She has the appearance of having been dreamed up only to provide someone to be Joseph Gleason's wife and I can't even confirm she existed. The facts we know about the wife of Joseph Gleason would fit the daughter of Edward better. The daughter of Edward Garfield is the only Abigail Garfield old enough to marry him that is found in Watertown records (where Joseph's Gleason wife was of, according to the marriage record).
So, how do we know Abigail, the daughter of Edward Garfield, was really the Abigail that married John Parkhurst? At this point, I'm left suspecting a bad assumption, since no references to primary evidence are given in Bond, Cutter, or even Anderson.