This was noticed on our live install of 2.8.7+ but I installed a clean fresh copy of 2.8.9+ (Build: 20151119) for testing.

As a teacher create an assignment and save without changing any options. Click on the assignment name then View/grade all submissions. Note that the Last modified (submission) field has no value. As a student click on the assignment name (don’t do anything else, just click the assignment name from the course).
As teacher refresh the View/grade all submissions page and note that the Last modified (submission) date has now been updated even though the student did nothing but click on the assignment name and made no attempt to submit anything.

Wait a few minutes and then as a student click on the assignment name again (repeating what you did previously). As a teacher refresh the assignment grading page. Note that the Last modified (submission) date for the student has not changed (i.e. it is not reporting the last time the assignment was "touched" by the student)

If an assignment submission is overdue the status field displays a message saying X hours x minutes late where those values are calculated from the Last modified (submission) value. If the student has never clicked on the assignment and so not generated a fixed last modified (submission) value the message shown is Assignment is overdue by: X hours X minutes, where that value is dynamically calculated from the due date.

This behavior is misleading as it is showing a modified value where a student has done nothing to directly modify anything. It does not act as a record of when the student clicked on the assignment name in the course as repeating the same action does not update the value. It results in a misleading status message that implies that a submission was made (late) but no submission has been made.

This behavior appears to have been introduced between Moodle 2.7 and Moodle 2.8, possibly as part of
https://tracker.moodle.org/browse/MDL-46171

In mod/assign/locallib within the get_user_grade method there are calls to
$this->get_group_submission($userid, 0, true);
The third parameter is create and was changed from false to true between Moodle 2.7 and 2.8
See locallib in this diff
https://github.com/moodle/moodle/commit/9e3eee671f75e3c582cd01863bea963e780ecf9a
I have reproduced this behavior with Moodle 2.9 and 3.0. When I toggle the parameter in the calls
from
$this->get_group_submission($userid, 0, true);
To
$this->get_group_submission($userid, 0, false);
The issue does not seem to manifest, but I have done nothing but one visit as a student to confirm that.

This item reports something similar as a bug but I cannot find a report of exactly this issue
https://tracker.moodle.org/browse/MDL-51142