And freedom of the press in the United States is protected by the First Amendment to the United States Constitution.
This is where Avenatti appearing on hundreds of television segments and having his name published tens of thousands of times since February is the saw that cuts both ways - he is now a 'public figure'. The legal hurdle for a public figure to successfully prove malice against the press is a pretty steep one.
So, the entire world currently watches Avenatti. And Avenatti publicly threatening to sue a very modest media outlet for looking at public records about his past is only going to invite more media scrutiny. The mainstream media can tear him down just as fast as it built him up - it sells advertising.
https://en.wikipedia.org/wiki/Defamation#United_States
