Hush made himself look like Bruce a while ago, hoping to kill him and replace him.
Now he came back to try to bankrupt them by claiming to be Bruce and giving away money publically.
The Bats are sticking to the story that Bruce is alive and well, presumably so there's not a story of Bruce dying at the same time as Batman, so they didn't challenge Tommy publically when he said he was Bruce, but are now keeping him in control.