ATC assures separation...
This is a pretty critical misconception. ATC does not necessarily provide separation, just because you are flying IFR. Let's do a quick recap of the different airspace classes.
In class D, ATC will provide separation between two IFR flights, but will not separate VFR flights. All flights are provided with traffic information, and must avoid collision by means of traffic information and a visual lookout.
In class E, ATC will provide separation between two IFR flights. Traffic information about VFR flights will be provided if possible - but VFR flights can fly in class E without any radio contact, so ATC might not know about all flights. It is up to the pilots to avoid collision by using traffic information and keeping a visual lookout.
In class F, no separation is provided, regardless of whether you are flying IFR or VFR. ATC will provide advisory service towards other IFR flights, and traffic information about VFR is possible.
In class G, no separation is provided. Traffic information can be provided as far as practicable. (In some countries, you are not allowed to fly IFR in class G airspace - but this varies).
So yes, pilots are expected to keep a visual lookout, also when flying IFR. Obviously, in bad weather, this does not really apply. This is also the reason almost all aircraft are equipped with anti collision lights and navigation lights - so that other flights can see them.
Additionally, ICAO Annex 2 (Rules of the Air) states:
An aircraft operated on or in the vicinity of an aerodrome shall, whether or not within an aerodrome traffic circuit, observe other aerodrome traffic for the purpose of avoiding collision.
Note that there is no mention of flight rules. This procedures applies to "An aircraft" - that is, any aircraft.