When people asks for "facts" or want to "wait until more facts come out" are they basically saying they want a source that agrees with their own biased opinion?

Not necessarily.

Sometimes when dramatic events occur, the reporting/media coverage at the beginning is haphazard and confused, and it's best to wait unti things settle down and some of the early rumors get dispelled or confrimed.

Of course, if you're talking about a subject like anthropogenic global climate change, your are exactly correct.