I'd let my training supervisor know what was going on. Then I'd have a talk with the trainee.
1. Name your specific concern in detail (sounds like situational awareness/officer safety issue).
2. Tell him you can not, in good conscience, recommend him for next phase due to him being a danger to himself and others. Tell him you will not pass him in this condition.
3. Tell him it doesn't matter if he thinks the problem is real or not, it IS real and you both need to work on it. Tell him you and the Dept. are willing to work on it with him, but it's ultimately his to attain.
If he grasps what you're concerned about, ask him what he thinks it will take for him to become aware. Involve him, but you and your supervisor decide what may work. Document it all. You should already know what learning style he prefers. Your co-workers or I may have some ideas on methods to get through to him. If he can't perform to reasonable 4th-week standards, you simply make your recommendation for remedial/prescriptive training and let the supervisors handle the issue. You did your part.
If he doesn't get it at all or thinks he knows better, make sure your supervisor is aware/involved. Do your best to make him aware, continue to document thoroughly, recommend remedial/prescriptive and leave it to your supervisors to decide.
If you have doubts about his ability to recognize/act, hunting for combative subjects you may/may not find is dangerous for him, you, the Dept. and your career. Train some more and see where you get.
-josh