I don't remember the scene with Pete but I would think the two scenes are connected. Both Ben and Pete sensed Josie. Does it matter if she is actually "seen" - just sensing her is just as significant. 

Every time this "Josie trapped in the hotel wood" thing comes up there are always many people who think the idea is ridiculous, impossible... Understandable, it is indeed ridiculous, but didn't we all see Josie in the knob? If they tell us that she's trapped in the knob...why can't she be trapped in the walls, the whole hotel?

And the alternatives that are usually posted are that "It's just a mystery we'll never know" or "Josie in the knob was just an artistic touch with no particular meaning", etc. Nobody has written a plausible alternative, based in what we see (knob, Ben, Pete) and what we know about the circumstances of Josie's death, her body weight, etc. AND the wood holds many spirits, isn't it Margaret?

Unlike the other dead or departed characters, she's conspicuously mentioned multiple times after her demise by several different players.  It struck me as the writers still wanting to keep her memory in the show's narrative as a possible later plot arc that never got the chance to emerge.

Got up early, found something's missing/ My only name/ No one else sees but I got stuck/ And soon forever came

Agreed, although I can't imagine why anyone would want to bring her back.