Grid MORA is the altitude at which you will clear all obstacles in the area of the grid by either 1000ft (if highest obstacle is 5000ft or less) or 2000ft (if highest obstacle is higher than 5000 ft.)
MSA are the altitudes at a radius of 25NM from a radio fix (usually the fix being used for the approach or the main fix, usually VOR, at the airport) that assure clearance of 1000 ft above all obstacles. And it is given for different sectors around the airport, hence the name.
Using Grid MORA as the minimum altitude when you are in the vicinity (i.e. within 25NM) of the aerodrome makes no sense.
1. The aerodrome may be at the intersection of 3 or 4 different grid sectors
2. The MORA may be for a point that is miles away from the airport
3. the MSA gives you a better picture (read situational awareness) of the terrain around an airport, allowing for better planning.
Take Beirut for example. To the west of the airport is the Mediterranean sea at an alt of 0 ft. To the East are mountains stretching up to 11,000 ft. You would never be able to get the whole picture simply by looking at the Grid MORA
On another note which company was this that made you brief minimum approach alts with Low Level chart Grid MORA? I would like to know so that I can stay the hell away from them. Looking at Grid MORA is a good way of getting an idea about the terrain for the extended area around the airport but not once you are in the vicinity of the field.