It sounds like your son went to court without an attorney.

DO NOT GO TO COURT WITHOUT AN ATTORNEY. EVER.

If you don't do anything else, make sure that fine gets paid on time, even if you have to help. Failure to pay will rack up another charge.

I imagine the officer downplayed the amount of the fine, either because your son was cooperative and he expected to include that in his case report, or because your son was upset and the officer needed him to calm down. The police officer making the arrest can suggest what type of judgement is appropriate, but the judge sets the final penalty.

I am not employed by NPS, but I can give you an idea of the thought processes involved in my area:

Bowhunters, and hunters in general, are expected to know the laws for the areas in which they carry their equipment. If the equipment is accessible and/or loaded, they are ready to hunt; if the equipment is cased, they are considered in transit, or not ready to hunt.
For example, Connecticut Statute 26-85: "...jacklight(ing) shall be construed as any artificial light when used...with...a rifle...a shotgun or...a bow and arrow...in any area frequented by deer...during the period from one-half hour after sunset to sunrise..." Artificial lights include car headlights.

After dark, people who are in areas which are posted "closed after dark," are trespassing. Yes, there are exceptions. "I was just leaving" is generally not one of them.

I am surprised at the amount of the fine, given your account. My guess is that there is an aggravating issue, be it regular poaching in the area, or something else.

Again, make sure the fine gets paid for your son's sake. Maybe get him a case for the bow.