According to Canvas documentation, quizzes are brought in to a new course space with their source status intact. This means that if it was originally "published" the quiz will be published in the new course space. Unfortunately this has allowed students in multiple courses in our institution to view the quiz content BEFORE the quiz was supposed to be open. This may be a deficiency in usage of Canvas as Teachers have the ultimate say in when a course (and its content) is published.
To allow for this oversight and/or human error, a choice to bring in previously published content as "unpublished" by default would be helpful. This could be implemented as a checkbox within the import content wizard.