If I change the URL for any remote repository (Repository -> Repository Settings: Remotes: Edit), Sourcetree wipes out information connecting my local tracking branches to any branches in that remote repository. The results appear to be equivalent to running the following set of commands:

git remote remove origin
git remote add origin new_URL

I would have expected Sourcetree to perform the equivalent of the following:

git remote set-url origin new_URL

NOTE: For what it's worth, a closer look at the repository tells me that Sourcetree effectively wipes out all information about the remote repository's branches (.git/refs/remotes/origin is empty) when I use it to change the URL for the remote repository.