The question of responsibility isn't always as easy as it might seem:
s DOC 8168 ICAO chapter responsibility
The pilot-in-command is responsible for the safety of the operation and the safety of the aeroplane and of all persons on board during flight time (Annex 6, 4.5.1). This includes responsibility for obstacle clearance, except when an IFR flight is being vectored by radar.
Note: When an IFR flight is being vectored by radar, air traffic control (ATC) may assign minimum radar vectoring altitudes which are below the minimum sector altitude. Minimum vectoring altitudes provide obstacle clearance at all times until the aircraft reaches the point where the pilot will resume own navigation. The pilot-in-command should closely monitor the aircraft’s position with reference to pilot-interpreted navigation aids to minimize the amount of radar navigation assistance required and to alleviate the consequences resulting from a radar failure. The pilot-in- command should also continuously monitor communications with ATC while being radar vectored, and should immediately climb the aircraft to the minimum sector altitude if ATC does not issue further instructions within a suitable interval, or if a communications failure occurs.
That's the reason we have minimum radar vectoring charts nowadays which ironically can't be used for position determination but it gives us some idea of what ATC is up to.
However some states in their respective national regulations still hold PIC responsible for it. Be sure to have read national R&R before accepting it.
Beware as well bout the fact of resuming responsibility for terrain clearance once DIR to was accepted. Many times ATC offers one short cuts in mountainous areas like LIME on ORI 6 Q departure which basically can be accepted under the presumption of following: PIC is solely responsible for terrain clearance once accepted and a/c is either above MSA or contingency procedure for climb out has been established.
Cheerio
