Crime Scene: What to do with a running system?

Are there any forensic specialists out there that analyze a machine while it is running at the crime scene before pulling the power? Why I am asking? I was sitting in a presentation this morning by a law enforcement officer who is said to be a court certified computer forensic expert. He stated that a machine should have its power cord unplugged upon seizure. Someone asked about dumping memory and his response was that it was saved in swap space and will be intact. I don't want to get into why this is not true, but I am curious how many people do live analysis before taking down a system. There is lots of juicy info available in memory and will be lost as soon as power is gone. Of course, if you have an idiot in front of the keyboard, more harm than good can be done. For a trained forensic specialist, I think they could get important information from the live system, document EXACTLY what they did and it hold up in court. Any thoughts??