A copy made with .copy() is shallow: the outer list is new, but the items inside are the same objects as before. That matters when the items are lists themselves:

grid = [[0, 0], [0, 0]]
shallow = grid.copy()
shallow[0][0] = 9
print(grid)

For a completely separate copy of nested lists, use copy.deepcopy:

import copy

grid = [[0, 0], [0, 0]]
deep = copy.deepcopy(grid)
deep[0][0] = 9
print(grid)
print(deep)

The same thing catches people making a grid with *. [[0] * 3] * 3 is one row repeated three times, so changing one row changes them all. Make each row separately instead:

grid = []
for i in range(3):
    grid.append([0] * 3)
grid[0][0] = 1
print(grid)