However even in a strict branching workflow, there's still a chance you'll have genuine integration failures when two branches are merged, even if they independently pass the tests.
There is a chance that the merge itself breaks the build. I must say that in practise we don't often see this. Maybe because we keep our branches small. Other people seem to be more aware of this problem https://gitlab.com/gitlab-org/gitlab-ce/issues/4176
My command line git workflow should not require working through a GUI.
Now, if this was added as some git hooks, enforcing the policy from both the command line and GUI then I'd be impressed (and excited).
https://bitbucket.org/tpettersen/bitbucket-build-status-hook
That way if I update master before starting on a new feature, I get a notification if the tip of master is broken (or still building).
Furthermore, using their UI doesn't guarantee that pipelines have been setup to test the commits in the repo. The article actually is about bitbucket pipelines, but hardly illustrates any of it.
I hardly use the web UI of remote repos unless I have to submit or review PRs. Especially the bitbucket UI which I find lacking intuitiveness when you start navigating the repos.
So, instead of branching from trunk I would branch from tests-pass and that would be guaranteed to have been tested and pass, e.g.,:
$ fossil branch new my-new-feature tests-pass
I even added some CSS to make this look fancy: http://www.rkeene.org/viewer/tmp/fossil-with-tests.png.htm