Love doesn't hurt - losing a loved one hurts! True love? Well, I think if we love someone enough, we would die for them! When Romeo and Juliette couldn't be together, they took their own lives! This is a bit extreme! And fiction! But if we are madly in love with someone, and we lose them, a part of us dies! Sometimes we think we'd rather be dead than live without them! That's what I think your saying means!

You are partly right, love really hurts when it touches you, and will develop into true love after more and more memories accumulated. True love really kills, it kills other love interfering you with your true love and make you loyal to your love partner. But sometime if love is out of control, it also kills ppl.