I suggest breaking the question down into pieces.
First, I suggest the complete information concerning Thomas Curtis's marriage to Eunice Peet be included in his biography:
"Thomas and Eunice Peet, both of North Stratford, were married on October 21, 1790, in the Congregational Church of Huntington, Connecticut."
It is important that you include his residence in North Stratford as it is very relevant information to determine the identity of his parents.
Then the first question is what Curtis families lived in North Stratford in 1790 who could be his parents?
The answer is a few Curtis families who are ALL descendants of Widow Elizabeth Curtiss (and her husband John Curtis) who were among the earliest settlers of Stratford about 1639. This family was the only Curtis family in Stratford and the adjacent Connecticut coastal towns at that time. As the population grew, families moved inland and settled areas such as the northern area of Stratford known as North Stratford in 1790. Not surprisingly, Curtises are found among the families of North Stratford. While other families moved into the area, no other families named Curtis are documented in North Stratford by 1790. The Curtis families in the 1800 census of Trumbull (the name North Stratford was given when it became a town in 1797) are in fact all documented descendants of John and Elizabeth Curtis. Consequently, I suggest the biography include the following:
"All of the documented Curtis families who lived in North Stratford in 1790 are descendants of John and Elizabeth Curtis. Consequently, Thomas Curtis is very likely the son of one of these Curtis descendants who lived in North Stratford."
Voluminous historical records of the Stratford and North Stratford area validated by the 1800 census records support this. Plus, it is very relevant to the identification of Thomas Curtis's specific parents.
Final question is which Curtis family is Thomas Curtis's parents?
First, I suggest you rewrite the Research Notes from the historical perspective and include the following accurate description:
"When Harlow Dunham Curtis compiled his 1953 Supplement of the Curtis Genealogy (ref), he included the following under the entry for Nathaniel and Mary Curtiss on p. 34:
Nathaniel and Mary had only three children of record. [Charity, Andrew, Everard.] Perhaps a fourth child was that Thomas Curtiss of N. Stratford who m. October 21, 1790 Eunice Peet.
Nathaniel and Mary Curtiss are one of the known Curtis families who lived in North Stratford in 1790. Harlow Curtis did not document why he listed Thomas Curtis under this particular family and his use of "perhaps" indicates relatively low confidence in his choice. At the time, Thomas Curtis had no known descendants so it was not that important who were identified as his parents.
Since that time, Lee R. Christensen identified Thomas Curtis as the likely Curtis great-grandfather of Vice President Charles Curtis. He also recommended that others take a closer look at the likely parentage of Thomas Curtis now that he has likely descendants. [ref]
In 2021, a descendant of Nathaniel and Mary Curtis also named Thomas Curtis analyzed the existing information about the Curtis families of North Stratford based on the 1953 Curtis Genealogy Supplement. Based upon observed family naming conventions and gaps in births, he came to the conclusion that Mitchell and Phebe (Peet) Curtis are the most likely parents of Thomas Curtis. An excerpt of this analysis follows: [Text currently provided in Research Notes.]"
This includes the original association of Thomas Curtis as the child of Nathaniel and Mary Curtis, its consistency with Thomas Curtis's North Stratford residence in 1790, and the degree of confidence in his choice. I don't think it is necessary for you to reference other genealogy sites that are likely just basing their placement on his choice. I don't think it is necessary for you to include theories that don't address Thomas Curtis's North Stratford residence in 1790 but if you do you should note that major flaw.
Regarding 'proof,' I don't think it is wise to use 'proved' or similar words particularly when conclusions are based on likelihood. Using words such as 'most likely' will better attract constructive future efforts towards improving likelihood rather than efforts focused solely on disproof.
I request that you connect Thomas Curtis to his most likely parents among the very few possible North Stratford families. Leaving him disconnected, along with the current version of the Research Notes, leaves the impression that we have no idea who his parents could be. That's far from accurate.