Like said in a previous post by glendalegoon, the magic phrase is "RADAR contact", once you've been identified descend is on me/the controller, and I'll add for wind and temperature as well.
Where I work, the MSA is 5300ft, but once you're on radar, we can take you down as low as 3100ft in certain areas. But when the radar is out for maintenance, or power cuts (happens, rarely but it happens). Then it's the 5300ft and then YOU, being the pilot, have to add for temperature and wind aloft, we help a bit by stating when giving the MSA that it's not temperature corrected.
We have a few that adds for temperature and wind, even when under radar control, fair enough, it's always better to be safe than sorry. We just notify it's already been done and everything is smooth again.
But be carefull, there has been accidents through the years where aircrafts has crashed due to the pilots not understanding that they themselves were responsible for terrainclearance.