The blog article can be found here - https://familysearch.org/blog/en/deletingpersonentries/
Deleting Person Entries in Family Tree
October 19, 2015 By
Contributors to FamilySearch Family Tree, particular those that are new to it, often hesitate to make changes for fear of “messing things up.” A common change that can cause real angst is deleting an individual. A recent change to Family Tree should help ease this worry, and safeguard against the accidental or incorrect deletion of persons added by others. FamilySearch has made deletion open only to the user that added a particular person to the tree and if that person has no other contributors.
What you’ll See
If you try to delete a person from the tree that you did not add, you will see a new alert that explains why you can’t delete the person in question and provides some alternative actions:
As you can see, there are some good steps to take to improve the relationships in the tree without deleting. If those options don’t work or if the person is fictitious, you can contact FamilySearch Support to have the data removed.
The purpose, and beauty, of FamilySearch Family Tree is the fact that it is a single, worldwide family pedigree, open and editable by all. Hopefully this new change will improve accuracy and consistency while at the same time encouraging all users to be comfortable making changes.