Hi, we've had the same problem here with our courses. Our kids should always have the possibility to edit their assignments. Now I had the time to look into the code and found out that it's an upgrade problem. We use Moodle 2.3.1
When you disabled the Button 'Send for marking' in the old assignment, the Variable 'resubmit' was set to 1. When I looked into mod/assignment/upgradelib.php line 93 there is the line $data->submissiondrafts = $oldassignment->resubmit;
But setting 'submissiondrafts' to 1 means exactly the oposite 'yes I wan't to have those two Buttons and if a student clicks on 'submit the assignment' he/she has not the chance to edit it again.'
The workaround for us was to upgrade to the new assignment, then change the setting in the new assign to 'Require students click Submit button'-'No'. Then tell the pupils to click on the 'submit' Button and the next time when they try to edit the assignment, there is only the 'edit my assignment' button left.
I will add this as a Bug into the tracker