Depends on circumstances. MUI means that your spell can have multiple active instances without causing any undesired behaviour. That doesn't neccessarilly mean that it has to be cast by different units - it can be one and the same unit!
For example let's say your spell places a 15 second debuff on the target. The spell's cooldown is 3 seconds.
Even if your hero is the only unit in game using this spell, if he casts the spell while another instance of the spell is already active (= some unit is already debuffed by it) and that spell is not MUI, an undesired behaviour will happen.