There is no need for a permit if the student is not planning to buy a gun. Even IF you require a background check, what will that accomplish? People who know they can't own a gun aren't going to take a safety class HOPING they can get a permit.
Actually just the opposite is true.
People who know they can't own a gun will take a class or rent a gun in order to get an otherwise unobtainable firearm in their hands.
Let me make something clear, I do not support additional background checks, classes or other restrictions.
The reality though is that people that can not otherwise possess a firearm, and intent on suicide using a firearm will try anything possible to get their hands on a firearm.
Statistically the person that commits suicide with a firearm (at a range or class) falls into certain parameters.
1)Usually they are alone.
For this reason most ranges that rent guns will not rent a gun to an individual.
If you're with another person, they'll rent you a pistol.
Now if you bring your own pistol, you can shoot there with no problem, even if you're alone.
2) People that own firearms do not typically go to a range to commit suicide if they decide to commit suicide.
There are other factors but these two relate to the current discussion.