after months of the budget being reported at $13M, deadline came out with an article and in it speculated the budget was $30M based on salaries. However they also said Jen got $15M and each of Bardem, Pfeiffer and Harris got $5M. Which, aside from being unlikely on its face given the type of movie, would also total $40M not $30M, so they didn't even convince themselves.
However, on the promotion tour, Aronofsky several times said he was allowed to do whatever he wanted in part because the budget was so very low. In one case he said in Black Swan he was able to do whatever he wanted because the budget was very very low, and similarly in mother! he was able to do whatever he wanted because the budget was very very low. The Black Swan budget was $13M.
So I don't believe it was $30M. You are free to believe it, and I agree that often you have nothing but BOM to go by, so that is the standard people use.