There's a component of "being stuck" to sitter, and the same (in the active version) goes for sätta: it can sometimes mean "attach".
A likely context for sätt den på väggen could be about a poster or wall calendar.
I believe that you can "sätta upp" e.g. a TV, an ornament or a bookshelf on a wall. This is perhaps not the first term that a native Swedish speaker would use but I'm pretty sure I've seen it being used in this context.