I am the professor who wrote the blog post.

What you mention was a very big problem for the adoption of services like Turnitin. In fact, when there is a match, there is no way of seeing the "source" of the homework, unless you get a permission from the "owner" of the homework.

Also, students when they submit the assignment to Turnitin, they assign a license to index the content for plagiarism detection purposes, and for nothing else.

And students have the right to remove their assignments from the index, if I understand the language of the agreement correctly.