Ok, now par the end of this article (or already at the beggining, because of the title) toi might be calling me crazy.
But my theory is this:

What if Parker wasn't a ghost/hallucination?
I mean, at first I did really believe he was just a figment of Booth's mind, because of the drugs and stuff.
But we do see along the episode that Parker makes physical stuff (like getting an object that was deep in the water, like carrying the lantern, like opening the hatch!) - I mean seriously, what a hell of a good hallucination, that makes that kind of physical stuff.
At first I accepted all this, but when at...

Pilot [1.1]

Brennan: Tell me toi tried "excuse me" first.
Angela: Ah, Sweetie. Yes, I did. Welcome home. Are toi exhausted? Was Guatemala awful? Was it horribly backward?
Brennan: And yet, I was never reduced to flashing my boobs for information.

Angela: toi know, diving head first in a pit of cadavers is no way to handle a messy breakup.
Brennan: Angela, nothing Pete and I ever did was messy.
Angela: [laughs] Then toi weren't doing the right things.

Brennan: Look, I am sorry if I embarrassed toi in front of your friends, but suivant time toi should identify yourself before attacking me.

DHS Officer:...