Well, I guess it doesn't gain access to sources of information it didn't have access to before. However, now it has the obligation to use sources of information that maybe it had no reason to use before. So if you want to give it special insights, feel free.
There's a section on ghosts hiding in the rules for what happens when a PC dies. Start there. You can see that the game loves "here's what's typical, but nothing is ever exactly typical," so go ahead and treat every individual ghost as exceptional in some way.
Just remember that your job isn't to keep the players in the dark, so you can have the ghost tell them whatever you think it should tell them.
-Vincent