What do we mean when we say it today?
Nowadays, we say "the course of true love never did run smooth" in exactly the same way. Love hasn't changed much in the past 400 years. It's still a bumpy ride. Usually when this phrase gets busted out, it's comforting someone about a rough patch in his or her relationship. Or a break up.
Just like Lysander, we try to make people feel better by blaming it all on love. This isn't "It's not you; it's me." This is: "It's not you; it's love."