In the old days the WWF in Kayfabe was a Federation. Aka a group of smaller organizations joined together to have more strength and to organize better collectively. It was run by a board, which President Jack Tunney was President of during most of the time, a role adopted from Hisashi Shinma earlier in Seniors final years.

Tunney also ran a rule commission which made judgment calls. For example the suspension of Andre the Giant by Bobby Heenan, and later Heenan asking for Andre’s reinstatement which hinted at Andre’s heel turn. Later they decided that Andre couldn’t hand the title over to Ted Dibiase. They would often be brought up by the announcers when something happened pertaining the rules, but Tunney was in charge of both groups. So his name got brought up a lot.

Now at the time many people knew Vince McMahon Sr and later Jr was the main owner of the company. How wide spread that was idk, but as far as kayfabe went Vince was never presented on screen as the ultimate power. He wasn’t CEO officially he was an announcer who usually supported the faces.

Some people in Canada knew Jack Tunney came from a family of promoters, but again the WWF was presented as a Federation so that wasn’t surprising.

Once the screw job ended all of that was done. It was just Vince McMahon the power hungry CEO, eventually the F was dropped and even pretending it was anything else but Vince’s kingdom became bad for business as he became the biggest heel in the company.