Random Appropriation of the Day! Dreamcatcher=all inclusive Native traditions
But there's a wealth of covert messages beneath the overt message. Among them:
Here's the actual story behind the dreamcatcher:
The Ojibwa believe that a dreamcatcher changes a person's dreams. According to Terri J. Andrews, "Only good dreams would be allowed to filter through. ... Bad dreams would stay in the net, disappearing with the light of day." Good dreams would pass through and slide down the feathers to the sleeper.
A dreamcatcher's purpose is to provide a good night's sleep. Which is about as related to health as a fluffy pillow is. The sign implies that Western traditions will cure you with medicine (pills) while Native traditions will make you comfy in bed.
All in all, the sign is a failed attempt to convey a multicultural message. The dreamcatcher isn't much closer to a symbol of healing than a feather, a pipe, or a rattle. I'm not sure it's possible to convey a multicultural message of healing with images only, but this isn't the way.
For more on the subject, see The Basic Indian Stereotypes and "Primitive" Indian Religions.