Facebook: Public Space or Private Space?

A woman has been fired for using facebook while taking the day off work. The intriguing bit is that she claims her employers created a false profile to 'friend' her and spy on her. Whether or not that is actually what happened (the company deny that it is), I wouldn't be surprised if it were common - many employers will just find it irresistable to keep tabs on their employees.

I'm mainly interested in how this compares to real world interactions of a similar kind. If she had taken the day off work and was spotted talking to a friend in a cafe, presumably this would not count as an invasion of privacy, whereas if someone from work had spied on her through her bedroom window this would be completely unacceptable. So where does facebook fit in here? Is facebook interaction public or private?