"you will get sued for violating the commercial-distribution aspects of copyright law"

I think that's incorrect. I think this would be infringement due to it being considered a public performance, not commercial distribution. As the copyright act says, "A public performance or display of a work does not of itself constitute publication."

The MPAA also describes the situation as a public performance issue:

http://www.mpaa.org/contentprotection/public-performance-law

Do you know of any cases where a public performance was prosecuted as a commercial distribution case?