I'm pretty sure the argument "if you invite someone into your house, you're responsible for their illegal actions" is plainly incorrect, but I'd be happy to see a citation of that statute.
There is a common exception in law for utilities. The power company is not responsible for whatever nefarious activity is enabled by supplying power. If you have an illegal marijuana grow operation the power company doesn't get prosecuted nor are they responsible in law for proactively identifying those growers. ISP and service providers don't want to be utilities because that requires that they provide a level playing field to their customers, but their business has all the characteristics of a utility and their customers would pretty much all prefer that over the current situation.
You may not legally be held liable though in many cases you can. It's a common trope within law and I'd guess derived from common sense that if you host illegal content then you are therefore bound to scrutiny for potentially enabling it. So by extension, if you care about being a free person, you are responsible for it. Anything illegal in my home and I'm bound to scrutiny and law. Why should big co's get a free pass? To me, I couldn't care less either way but consistency in law would be just lovely.