Well if you think about it, there are 8+7+7+6 = 28 tiles (43%) on the edge of the board, and another 6+5+5+4 = 20 one away from the edge, for a total of 48 (75%) within 1 tile of the edge.
Of those 48 tiles, a full 1/3 (25% of the whole board) are within 1 tile of a corner. So in short your odds are (assuming you haven't strategically saturated the board with specials/wrong colour tiles)
25% within 1 tile of a corner
50% within 1 tile of the edge but not near a corner
25% more than 1 tile away from any edge
So in short, it's both. It is indeed random, but it's also (almost) always going to end up on the edge.
I suspect this is why they eventually had to specifically make an exception for Punisher's green random 3x3 block.