I started saying it because it didn't take me long, especially in relation to the people I met in the Hospice grief support group that I attended, to realize that EVERY experience with grief is different. You could put two people in exactly the same series of experiences and because each of us has such a different set of tools, emotional vulnerability and access to support, there is just no way to compare the pain.
I stopped saying things like, "I understand because . . . (fill in my life altering painful experience here)." I started stopping at, "I'm so sorry for your loss," and then trying to listen and really hear and respond to the other's expression of pain.
Giving up the concept that there needs to be comparison or understanding to sit with anyone, in that moment, and just share in their pain has led to some really loving and intense moments with people I will never really know.
It also gave me permission to feel the grief I need to feel. Surviving those trials by fire, concentrating on the fierce love that gives me those connections. That's been worth the pain.