It's YOUR friendship, and I would hope there are not people who tell you with whom you can be friends.
However... understand that you both have baggage, and you should only have to carry your own. If you realize that she's using you, even unintentionally, for help in carrying her baggage, then you should drift away. You are not a trained counselor; let her deal with a trained counselor instead of making you feel responsible for helping her.
That being said, if you enjoy the same activities, love taking walks in the park, etc., then enjoy! Just keep it "non-hospital content related," and you'll be fine. :-)