If the image is in only one collection, you only see the badge if you are viewing the folder that the image is in.
If the image is in more than one collection, you get the badge, no matter where you are. That probably explains why you have a picture with the collections badge.
Clicking on the badge shows what collections that image belongs to.
I just started to use Lightroom 4. Every photo I have in the catalog has been placed in a single collection within a collection set. Neither the photo in question, not any other photo, appears in two collections. Yet, only this photo displays a collections badge to the single collection it is in. Your comment about not seeing a badge when a photo is in only one collection was helpful. But why is this one photo not treated like the others?
Any chance you've (inadvertently) added that single photo to the Quick Collection? Remember you can do that simply by clicking on the image in the grid or filmstrip and accidentaly hiiting the Quick Collection icon in the top right-hand corner,
If you click on the Collections badge for that one image, it will list all the collections that it is in. Have you checked that? What does it say?