A distributed team member who understands the big picture will work towards accomplishing project goals and work around the hurdles. Team members who understand the big picture are less likely to give you excuses instead of deliverables.
Care should be taken to communicate factual and relevant information. I have seen some demand team members hyping up a project and providing very optimistic information about a client when no substantial information exists. That will back fire. So it is important to be enthusistic and at the same time level headed about it.
I read that Disneyland actually overstates the wait times in their rides so that when you get to the ride within 30 minutes instead of the stated 45 minutes, you actually feel good about the 30 minute wait. I won't comment on the appropriateness of that approach. But I believe it is effective. It is always better to share information with cautious optimism rather than promising something and not delivering.
Understanding the financial aspects of a project can help all team members make right design and development decisions. I'll write my observations in that area later.
Why is the big picture more important to remote team members than team members in the headquarters?
Big picture information is important to everyone. However unlike the headquarters team that can piece together the big picture using information gathered through informal networks and hallway conversations, remote teams rely mostly on planned communications to get their information.