If ATC clear you direct to a point, then they remain responsible for terrain seperation.
Beware, ATC are responsible for your separation ONLY IF THEY ARE RADAR VECTORING YOU. Being cleared direct to a point is NOT a radar vector: for it to be a radar vector they have to issue you a heading. As such terrain separation remains
your responsibility.
In answer to the question, if cleared off a SID direct to a point while still below MSA (and in absence of company guidance), it's up to the PIC to decide whether to accept it or not, and terrain separation is up to him/her.
The other night departing an unfamiliar Chinese airport, immediately after departure I was cleared off a lengthy SID direct to a point: being unfamiliar with the airport and the surrounding terrain, we politely accepted but only started our turn once above MSA. If it had been day VMC at a familiar field, different story...