Remember Atlassian in their infinite wisdom renamed the on-premises product formerly known as Stash to Bitbucket despite being a completely different code base to Bitbucket.com. I think they are talking about Bitbucket.com.
The bitbucket.com website gives a check box to select whether to close a branch though. Unless you mean that the on-premises product doesn't?
The on-prem one I use has checkbox when you merge. It's unticked by default.
The on prem version I was using a month ago had a checkbox, ticked the last way you checked it by default.
So if you merged feature -> develop -> master and remembered to delete feature it would delete develop by default as well...
So, if my company has a workflow where that box should always be checked or not, and rarely overridden by the user, ...