On the question of THAT FBI investigation, the only relevant element is: Did Gaetz travel with an underage girl without a guardian present? If so, they should interview the girl.
If not, there should be no investigation by the FBI or any other LEO. The fact the FBI pointedly refused comment indicates there is an investigation whether warranted or not.
Because when asked about a supposed investigation, the FBI will always say “no” if it does not exist.
Is Matt Gaetz a Child Sex Trafficker? Here's What the Law Actually Says
To make a case against Gaetz, they need to prove there was sexual contact of some kind. It's hard to see how they prove that absent a cooperating witness in the girl...presuming of course she wasn't 18. If she was 18, all of this is moot.