I have some questions about this as well. Take a look at this picture:

You can ignore the shaded squares, they show the true combat range. We are interested in the combat range + 1, which is the ant's influence. The influence is shown in each square using red & green numbers (top & bottom left of each square). A square should be safe for a green ant if the green number > the red number in that square.
As you can see, left of the bottom green ant should be safe & right of the top green ant should be safe as well, since the influence fields suggest 2vs1 in both locations. However, if we move the green ants there and the bottom red ant moves up 1 square, both of the green ants die (as well as both of the red ants), so these squares are not safe at all.
Another example is bottom green moves left, top green stays where he is. Again the fields suggest this should be safe, but again, both will die if the right red ant moves left and the bottom red ant moves up.
Am I calculating something incorrectly here?