Yes, but the flamethrower will now be very hard to use, since is a low range weapon that requires LOS. So if you use it, most of the time you will expose yourself to fire, and death.
This happened actually to me, and also them just walking out of fire to me and melee kill me, the second one may be fair, but is not obvious to think that you also need to lit the tiles between you and the enemy to be safe. The first has not counter and should not happen.
Yes that explains how some enemies walked trough fire diagonally crossing a tile, without taking any damage.