I didn't watch it, but the linked article displays the opposite:
"I have not had a relationship with a 17-year-old. That is totally false," Gaetz told Fox News' Tucker Carlson in an interview Tuesday night. "That is false and records will bear that out to be false."
His use of the word "relationship" was oddly specific. And in the same interview Gaetz claimed he had gone on a double date with the 17 year old "woman" and Tucker. I believe Gaetz was being blackmailed - but he also had something going on with an underaged kid.