The first image is the index database entry for Thomas Frame from Ancestry.com's "U.S. Naturalization Record Indexes, 1791-1992," who was naturalized in Cook County, Illniois, in 1873. This index entry indicates he was born in Ireland. The item from which this index entry was made (the black and white card below) does not indicate he was born in Ireland.
Instead it was created from an index card (shown below) that comes from National Archives Microfilm Serial Publication M1285 "Soundex Index to Naturalization Petitions for the United States District and Circuit Courts, Northern Distrit of Illinois and Immigration and Naturalization Service District 9, 1840-1950." The card actually indicates that the "country of birth or allegiance" was "Great Britian, Ireland." This does not equate to a country of birth of Ireland.
The index card is meant as a finding aid to the actual record of Thomas Frame's naturalization, not to replace it. Ancestry.com's "U.S. Naturalization Record Indexes, 1791-1992" is an index that includes index entries.
Another problem here is that the information on the record was "massaged" to fit database fields in Ancestry.com's index. Information on original records should not be massaged to fit database entries.
I have seen a copy of Thomas' naturalization and have written about it for Casefile Clues. Thomas indicated he was a subject of Queen Victoria of Great Britian and Ireland, but he makes no statement about his specific place of birth.