I'm sorry Bonj, but you're not being pedantic, you're just being incorrect.
Grid references must always be rounded down, what ever the value of the last figure you are dealing with.
All grid references are not actually points, but squares where the reference refers to the bottom left hand (south west) corner. Obviously the more accurate the grid reference (ie an 8 rather than a 6 figure reference), the smaller the square.
But as you reduce accuracy, you must still refer to the SW corner of the next largest inclusive square. So if you had GR369,139 (a 10 x 10m square) but only needed the accuracy of a 1km reference, it would become GR36,13 even though the original reference square was only a maximum of 10m from GR37,14.
But by rounding it up you are now saying your described point is in the square kilometre that lies to the NE of 37,14, which is untrue, it lies in the 1km square to the NE of 36,13.
It does make a difference. Searching for casualties in the wrong square is as frustrating as it is futile.