Beware, ATC are responsible for your separation ONLY IF THEY ARE RADAR VECTORING YOU.
Not according to ICAO. PANS-ATM 8.6.5.2 says:
When vectoring an IFR flight
and when giving an IFR flight a direct routing which takes an aircraft off an ATS route, the controller shall issue clearances such that the prescribed obstacle clearance will exist at all times until the aircraft reaches the point where the pilot will resume own navigation. (My bold.)
The usual caveats about division of responsibility apply.