We have a private pilot here in Oz who has claimed the following:
By the way, in the USA ATC's will separate IFR aircraft when in radar covered class G. It's only in Australia that ATC's are not allowed to do this and are specifically trained just to give a traffic information service.
and
in the UK, air traffic control actually “control” IFR aircraft in Class G. The Plymouth tower manned by air traffic controllers sits in Class G airspace. Those who want an IFR service are actually “controlled” by air traffic control – either in the Centre or in the tower.
In the latter quote, the context he has used "control" means provide a separation service in Class G to IFR.
In the U.S. & U.K. is this really the situation i.e. you separate in G??