That's backed up by copyright law. If you build a theater, charge people to enter, and program runs of classic movies, you will get sued for violating the commercial-distribution aspects of copyright law, even if you bought the DVD you were charging others to see.
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?
"But suppose you took the same movie or TV episode and showed it to patrons at a club or bar that you happen to manage. In that case, you have infringed the copyright in the video work."
Whether a public performance constitutes legal publication is, of course, a separate issue. The point I was making is that copyright law governs both duplication and distribution, not duplication only.