I've heard this a few times, that people with depression see the world in a very objective way. Can anyone explain what precisely this means?

I'll bet it has something to do with dopamine levels. Since the hormone is a part of our reward motivation system, and depressed people show lower levels, they may be saying a depressed person is less likely to fall prey to subjective influences.

"Just because you are paranoid does not mean they are not out to get you."

this?

 

http://en.wikipedia.org/wiki/Depressive_realism

They're less likely to rely on heuristics (mental shortcuts).

 

Mood and heuristics: the influence of happy and sad states on sensitivity and bias in stereotyping.

http://www.ncbi.nlm.nih.gov/pubmed/10870905

I've heard this a few times, that people with depression see the world in a very objective way. Can anyone explain what precisely this means?

Its a generalization that is mostly true. Lower dopamine levels means less likely to assign supernatural causes to phenomenon. There is less reason to need something to cause the observation.