My heart absolutely breaks when I read this. How hard to have this happen, and then to know that it could get worse if he turns them in. For now, I would respect your son's wishes. Here's why:
First, it will show him you are trustworthy. If you report this against his wishes and other things continue to happen, he might not tell you because he knows you'll report those as well. Make sure when you speak to him he knows that you understand where he's coming from and you will respect his wishes to drop it. This sets up/continues a nice trust between you two.
Second, it reinforces that he has some power in the situation. My daughter is only 10, but we've been starting to deal with the 'mean girl' stuff. My hubby gets so mad and wants me to talk to the teachers and call parents. I keep reminding him that there will always be another mean girl around the corner, and my focus is to fortify my daughter- as you are with your son. Keep talking to him about why other kids bully, and give him tools to handle it in the moment. If he'll go for it, role play some situations (maybe 16 y/o boys are too cool for this, but suggest it anyway). Keep reinforcing what he should do when things happen. This does include telling him the difference between what he can handle and what he can't- help him learn how to decide when a situation is too dangerous or out of control, and how to call for help.
As for you, you should keep a record of what happens. Even though you aren't filing charges, you'll have a history. I'm not sure if you can 'file' it with anyone without them taking action, might be worth checking.
Between the two of you, hopefully your son will keep telling you what's going on, and will know if a situation is beyond his control. And you'll know as well. Hopefully there doesn't come a point that you'll have to report something against his will, but you'll be prepared.
BTW, walking away is a good choice always, but sometimes bullies need to know that you'll stick up for yourself and not be an easy target.