Akiva, if the company is well-known enough that the inevitable scandal when the truth comes out would be picked up by the press, I would think about declining. It would be very easy for a reporter to write a story slanted towards the idea that the theater was tricking its audience, and if that happens, you don't want to be in the article as someone who was an active participant in a plot to deceive innocent people who paid hard-earned money to see live theater, only to be fooled by the theater management.
If it's a small theater that is completely off the radar screen, then it's a slightly different situation, but if not, I think the theater is crazy to entertain this idea. As you've pointed out, it won't work, and the theater will lose any audience base it ever had.
"What was the name of that cheese that I like?"
"you can't run away forever...but there's nothing wrong with getting a good head start"
"well I hope and I pray, that maybe someday, you'll walk in the room with my heart"