[Disasterpiece]

Your definition of "illegal content" may be what's the problem here...

adult content isn't illegal by it's own definition, but (depending on your countrie's laws) offering adult content to the general public without controlling who actually can access this content (like minors) may be an illegal offense, so if you keep this material to members (read: non-public) you circumvented this rule and should be ok with it.
And this is how you should approach this.

I can only speak for my own countrie's law, which is germany. So for example, take a mp3 file.
It's not illegal to own a copied mp3 file of a commercial song. So if I put it on my server and just leave it there without anyone being able to access it publicly, I have nothing to worry about. It's my private space and as long as it stays there, I'm safe from any copyright infridgements.

If i'd offer it publicly like forum attachments viewing by guests or by registered members, whereas anyone can become a registered member without my direct help (like adding them to a special usergroup), it's considered offering of copyrighted material and I can be sued.
If I create a special usergroup for my friends and family and people I know, it's a private group of people which I allow access of my files. This is also allowed, as long as I have control over whom I grant and revoke access to these files.
If I make money with this (like VIP membership) I can be sued because I make money with copyrighted material, regardless if it's public or not. Ofc. there still must be someone who actually files the fraud. Depending on the size of my forum/community and the traffic, it may be unlikely someone finds out, but possible nontheless.

The hosting company is by definition the one which even stands over the system administrator, because they have physical access to the machine/drives where the data is stored.
Depending on which hosting organisation you choose, most of them have a paragraph about privacy in their TOS where they tell you that they respect your privacy and only access your private data if they're ordered to do so, by a law firm for example. This is mostly the case with ordinary TOS.
Also, they make their money with your files. Normally, they aren't interested in the stuff they make their cash with, unless it disrupts their service or they are forced to investigate.

Maybe this gives you a better idea of that topic. Always know your rights!