He never made the claim publicly, he just gave some standard line about it not working out.
Before any interviews (with any candidate), Woody gave a generic "Rex is still our coach" line, but it was widely believed in NFL circles that if a candidate really wanted his own guy, that this wasn't an iron-clad decree (turns out that it was). In the first interview, they didn't even discuss Rex (or Bradway), it was more focused on how he would build a team, and if he was willing to trade Revis. Everything went well and he starting calling off interviews with other teams to focus on the Jets job. In the second interview to lock everything down, they got into discussions re: Rex, which is when Woody made it clear that keeping Rex was a non-negotiable condition. Additionally, he made clear that keeping Bradway in his current role was also a non-negotiable position as well (which is another fact that didn't make the papers, but was confirmed a few weeks ago by a Seattle based Jets fan on this forum who spoke with Schneider, who still keeps in touch with Idzik). At that point Gamble didn't want the job under those conditions and declined it. Days later, the NY papers come out with articles claiming he "interviewed poorly," which was obviously leaked by Woody.
FYI, there were no "football men" in the room conducting the interviews - it was Woody, Glat, and Akselrad.
I don't have NYDN or NJ.com links, but those are the facts. Regardless of whether or not one wants to believe them. I hope one day everything that transpired in that interview process comes to light, because there are quite a few people who have been advancing false narratives, and I'm not one of them.
Honestly, at this point maybe it would be for the best if you did. If something so innocuous warrants a ban in your eyes, then this probably isn't the place for me anyhow.
There are obviously moderators here who don't like me very much, and posting here is becoming less and less enjoyable and more and more of a chore. So if you could do me a favor and pull the trigger on that ban, I'd appreciate it Thanks in advance.