On tile 4A it has three diagonally adjacent blocked terrain boxes. They don't block LOS (as the example in the manual shows), but I was wondering if they block movement, diagonally. My group was playing and we decided that if you can shoot through it diagonally, then you can move through it diagonally. What do you all think?

yes they can be moved through diagonally. The movement example in the rules implies this, just replace one blocked terrain with a monster, and the other with a board corner