That would be true if the salt ice froze homogeniously but that's not actually what happens.
Salt water(3.5% NaCl) starts to freeze at roughly -2C and in a container, freezes from the outside in. The ice is fresh water(it's one method of desalination)with the residual, a more concentrated brine liquid pushed to the inside of the block.
As the temperature drops, the brine gives up more fresh ice and becomes more concentrated until -21C where everything freezes.
Below -2C, the brine is held in liquid pockets inside the fresh water ice, the exterior of the ice block is fresh water with a melting point of 0C.
The block has to completely melt to release all the salt.