According to .65 5-6-3 It CAN be done with various circumstances.
5-6-3. VECTORS BELOW MINIMUM ALTITUDE
Except in en route automated environments in areas where more than 3 miles separation minima is required, you may vector a departing IFR aircraft, or one executing a missed approach, within 40 miles of the antenna and before it reaches the minimum altitude for IFR operations if separation from prominent obstructions shown on the radar scope is applied in accordance with the following:
a. If the flight path is 3 miles or more from the obstruction and the aircraft is climbing to an altitude at least 1,000 feet above the obstruction, vector the aircraft to maintain at least 3 miles separation from the obstruction until the aircraft reports leaving an altitude above the obstruction.
b. If the flight path is less than 3 miles from the obstruction, and the aircraft is climbing to an altitude at least 1,000 feet above the obstruction, vector the aircraft to increase lateral separation from the obstruction until the 3 mile minimum is achieved or until the aircraft reports leaving an altitude above the obstruction.
c. At those locations where diverse vector areas (DVA) have been established, terminal radar facilities may vector aircraft below the MVA/MIA within those areas and along those routes described in facility directives.
Now, I believe WHY it can be done, is because the MVA provides certain clearances, just like the MEF on a sectional, it doesn't mean mean that the area elevation is at that height absolute throughout the entire sector, and if you follow what the .65 prescribes above it still ensures terrain clearance. For example, if you see a MEF of 25, that means there is something in that sector that is 2300-2400 agl, there is also area that is much lower than that. That is my take on that.
EDIT: It is one of those things that the FAA says is OK so it is. For example, why was it ok to give landing clearance with someone being put in position? Then there was an incident and it was changed. In this case whether you have 1 inch of clearance or 10,000 feet of obstacle clearance, you are still above the object. The question is at what altitude does the margin of error being unnacceptable. I would imagine there was some study that said If a controller follows X rules, then vectors below MVA is not a significant increase in compromising safety.
MVA and Departure
