In a newly created feedback activity, in a course that has not been accessed by the students yet, we were seeing status of "started" for some of the students when viewing non-respondents. Upon further investigation, we discovered that if you created a new feedback activity in any course and enrolled one of the "started" users, that user immediately showed as "started" as the status under view non-respondents.

I believe this is happening because when a user starts a feedback activity it creates a record in mdl_feedback_completedtmp and the query that checks that table for records is only looking for the userid and not the feedbackid as well.

Steps to replicate:

Create a course (Course A) with a feedback activity that is not anonymous and has 2 pages of questions.
Create a second course (Course B) with a feedback activity that is not anonymous.
Enroll the same user into each course.
Log in as the user and go to Course A and start the feedback activity by answering the questions on the first page and going to the second (this should create a record in the completedtmp table).
Now go into Course B (as administrator) and check the status of the non-respondents in that feedback activity. You will see that it says "started" even though the user started the one in Course A and not Course B.