Of course many of the above posts make a few assumptions:
Remembering that this is in Class G airspace, irrespective of the service being provided both aircraft involved the near miss would have to be on frequency (to be known traffic) or the controller would have to have radar contact with the other aircraft (to be unknown traffic)... it is possible to be ignorant of the presence of another IFR flight.
If traffic information was given under RIS, the responsibility for avoiding the other traffic rests with the pilot irrespective of Flight Conditions (although the pilot might reasonably expect the Controller NOT to pass further instructions that place him/her into confliction... which is where I feel the Approach Service arguement comes in?)
That the Controller may have offered advisory information before the near miss, but the pilot is under no obligation to follow that advice (under RAS or RIS in Class G)?
IMHO, therefore, if the pilot choses to ignore any given advise no responsibility for the loss of separation can lie with the Controller?