Sounds to me like your AV/IT department is going to the extremes with  
their position.

Stanford does a nice job of presenting the law (http://fairuse.stanford.edu/ 
) and your proposed usage should easily fall under the Fair Use  
provisions of copyright law. I've also attached the Society of Cinema  
and Media Studies Statement of Best Practices for Fair Use in Teaching.

Beyond that, freeware like Handbrake (http://handbrake.fr/) will allow  
you to rip material from a DVD. Then you can simply import that  
material into something like iMovie to edit the pieces that you need.

Good luck.

-chad


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Online resources for film/TV studies may be found at ScreenSite
http://www.ScreenSite.org