I don't have a strong opinion, not having studied this very deeply. But I would not call the Revised Merritt Records a reliable source in this matter. That work, and the History of the Cornelius Family, both have the maddening habit of the better compiled works from 100 years ago: listing excellent quality land records, probate papers, etc. and then right alongside providing other information that is simply listed with no hint of the informant. Or maybe they just write that the information was "reported," and say nothing else. It is hard to just dismiss this information, since these sources used good-quality sources that were hard to access for the other information.
The maiden surname of Mary seems to be one of these pieces of information. Is there any other source that John had married someone named Cornelius?
Even if so, was it a married name? Or was it a patronym? Perhaps her father was a Cornellis. Unless some other sources are forthcoming, I would think it appropriate to detach her and put notes on parents profile and her own indicating the lack of a reliable source.
Incidentally, I added a source to the profile of Arent Cornelius, giving an abstract of a primary source document confirming the statements about "Adrian" Cornelius captain of the Canary Bird.