The Scottish Premier League side were linked with a move for Johnson before the departure of head coach John Robertson.
The Tynecastle legend left the club last week after refusing to take an assistant role to another coach.
Anderton said: "People have been accusing this club of acting dishonestly and unprofessionally, but I would have to ask some of the guys in the media who had me meeting Gary Johnson.
"It is good that I know the guy now, because I had certainly never heard of him before.
"I was supposed to have been meeting with him and thrashed out talks.
"I had the manager asking who this guy was, and that was very disappointing.
"I also received a death threat off the back of it from a Hearts fan because I was meeting Gary Johnson and I was a 'yes-man' and all the rest of it."