In an educational institution, we make extensive use of the Fair Use Doctrine of the U.S. Copyright Law to allow us to use excerpts of copyrighted material for educational purposes and the courts have upheld this as Fair Use. However, the Fair Use Doctrine (http://www.copyright.gov/fls/fl102.html) clearly limits us to “…reproduction by a teacher or student of a small part of a work to illustrate a lesson…”.
Copying entire videos onto a Mediasite recorder would be a violation of U.S. Copyright law, even though only registered students can get to it. Those students could share the video with non-registered students.