There are several levels of "independence" when it comes to running a forum:
1. No independence: proboards, simplemachines, or some "free forum hosting" website gives you a free forum. Any of those "get your own forum in 15 minutes" websites fit into this category. They host your site AND maintain the software. Basically, your forum belongs to them and they are responsible for everything posted there. If they get the smallest complaint, they quickly shut you down first and ask questions later.
2. Some independence: You find your own (usually free) forum software and install it on your own web hosting account. This gives you a bit more freedom, but you are still at the mercy of your webhost. The complaints have to be a bit more serious (defamation, copyright issues, anti-semitism, etc.) but people could still easily find out who is hosting your site, and register a complaint. Webhosting companies can and will "pause" your website while these issues are sorted out.
3. Complete independence: You find your own software AND you host that software on your own web server. This is the most work, and it requires a lot of technical (Linux, Apache, SSL, modules, PHP, MySQL) expertise. There are other requirements, which I won't go into detail about here. But let's just say that technical expertise is just the FIRST hurdle you must overcome. But the level of freedom in this category is limited only by the laws of the United States itself. If someone has a problem with your site, they have to get a stack of money (measured in thousands of dollars) and hire a lawyer. Lawyers don't do contingency lawsuits for things like defamation. Or if someone threatens the life of the United States President, you might have recourse to the authorities. Things like that. But these aren't the kind of issues that have shut down so many Trad Catholic forums in the past...
CathInfo is in category #3. That allows us maximum freedom to discuss whatever we want. (We started out in category #2, and moved to category #3 in April 2016.)