In my experience, it was true. As house, bar, and concession manager of a theater, I was sometimes given special instructions on the selling of merch and refreshments from producers of shows. Of course, this was not on broadway, so perhaps the rules are different. I work part-time selling merchandise on Broadway, and I worked under a top producer for years. From what I saw, producers can make requests like "don't serve ice in the drinks because it makes noise," but they can't say, "don't sell drinks."
Similarly, I've worked shows where the merch and concessions people were asked not to "hawk" in the aisles because it disrupts the serious tone of the show, but they can't say "don't sell food." (Merch doesn't really apply here because that IS determined and earned by the producers, not the theater owner, but I am bringing it up because that is my personal experience.)
All concessions and bar revenue goes to the theater owner, NOT the producer.
However, it is also true that many theater owners are also producers (like the Nederlanders) and sometimes join the producing team in order to secure that show for their theater. So there you go.
In theater there is never an easy answer.
Nothing matters but knowing nothing matters. ~ Wicked
Everything in life is only for now. ~ Avenue Q
There is no future, there is no past. I live this moment as my last. ~ Rent
"He's a tramp, but I love him."
