It's just not true. Time doesn't heal anything if you don't deal with the emotional pain that is connected with a loss. Grief can take as long as a lifetime if you don't address the emotional wound. What happens when you don't do the emotional work is that one loss gets piled on top of another and you accumulate grief. The result can be major mental health consequences.
Accumulated grief can be very difficult to work with.
It can be enormously painful. When I first became aware of grief as something that people experienced in life, I thought that it was just about what happened when someone died. And those are the kinds of things most people think about when they think about grief. But this overlooks the fact that all of us face multiple losses in life. I'm thinking of a little girl who goes to school and somebody hits her and treats her badly.