The Clown Prince of Crime
Super Freak
The Ghostbusters are indeed famous by the point they hire Winston but no one believes them.
The public at large think they are scam artists who have ridden to fame on a bunch of made up nonsense. It's the 80s, there was no footage of anything on TV up to that point that proved they were really busting ghosts and the handful of people they helped couldn't hop on Reddit and post about their experience.
You guys may not remember, may be too young or from russia...but there was a ton of scam artists on tv in the 80s. This one guy would convince children via tv commercials and buying air time, to steal/send their parents jewelry to him.
Even Winston's reaction to being hired makes it clear he doesn't understand what he's getting into. Janine asks if he believes in paranormal and his response is that if there is a pay check, he'll believe anything, indicating he's willing to go along with, what as far as he knows, is the lie they're perpetuating.
It's why Peck wants them shut down, why the cops are on his side, why the mayor needs convincing... etc. I mean, even Dana is skeptical and she saw actual ghosts.
Now Ghostbusters 2 is a different story. For the kids at the party to still not believe that Mr Stay Puft happened when they had actual tv cameras at that event at the end of 1, doesn't make sense. But Ghostbusters 2 is pretty meh in general.
I don't know what the public perception was because the film didn't really explore that angle. The media seemed to be on their side for the most part, since they were featured on tv shows and magazines. Business was booming, and even if it's true that a percentage of the population thought they were scam artists, there are always those who fall for the scam artist and blindly believe. They were popular and in need of help, so you would think there would be a lot more people in NY city interested in making some money and being famous, not to mention that there must have been more people out there who truly believed in the paranormal, plus the percentage of the population who buys into the scam artists.
Also, Walter Peck was an inspector for the Environmental Protection Agency (EPA), and the reason he wanted to shut them down was not because he thought they were liars or stealing people's money, it was because the EPA wanted to assess the Ghostbusters' operations for any possible environmental impact, such as the the presence of noxious, possibly hazardous waste chemicals created by the storage facility and their equipment.
It was only after Peck messed up by blowing up the facility, letting all the ghosts escape that he lies and blames the explosion on the Ghostbusters and accuses them of being scam artists, even though at that point, there are so many ghost incidents going on in the city, that it's clear that it's not a scam.
