Here's the thing. If you hit someone/thing it doesn't matter whose fault it is or who was responsible for separating or any of that, because in all likelihood you are now dead. So at the end of the day, only YOU as the, or one of the pilots of an airplane are responsible for everything, including traffic separation. The term final authority comes to mind. Also the phrase "you don't want to be dead right".
To go off on another tangent this is also why situation awareness is soooo important. Just flying the airplane is not enough. Especially in a busy traffic environment you also need a picture of everything going on in your head. Both controllers and pilots make mistakes. Even in IMC you have some responsibility for separation, in that you have an idea of what is going on. If a controller clears an airplane for the ILS and then clears you for the ILS a few seconds later and you're only .5 miles from the FAF something is wrong, and while it's the controller's mistake, if you end up dead it doesn't really matter whose fault it was. Or terrain and IMC, a really good example of that is the ACE Dillingham 1900 crash last year about this time. The controller was likely at fault there, but hey the airplane was IMC and terrain separation(via altitudes given) is the responsibility of the controller right? Well, yes but they're still dead.
How about ATC is being nice and gives you a vector 200nm, "proceed direct when able" to your destination while IFR. You lose coms after a bit because it's an area of shoddy reception. Problem is the winds aloft are a lot different than that vector accounted for, say 50knots in the wrong direction, now you're going to be severely off course while having no coms for 20 mins and possibly below terrain in the new area you're flying through. It's your responsibility to correct that vector in order to not hit terrain.
I guess the point is, if you rely soley on ATC for anything, you're gonna have a bad time. Everything from navigation, terrain and traffic separation... EVERYTHING is at the very least jointly responsible if nothing else because it's your ass in the seat.