They are 13 and are too old to find backyard camping fun. The friend has never been camping or fishing.
We took DD14's friend camping with us last year - it was her first time ever camping and she LOVED it!
Well, other than the fact that it was 103 outside, and she got super sunburned and it thunder-stormed so bad the 2nd night that we literally woke up in a pond in the tent....but guess what - a year later, both DD and her friend laugh about it. What an amazing memory, and that was just a little camping trip. And they are girls....and both of them loved going fishing on that trip.
Don't assume! Kids who "have it all" often love new experiences that they wouldn't get otherwise. My kids are I guess what you would say middle-of-the-road. The have everything they need and some of what they want. We have been to Disney twice, but we will never make it to Europe or really anywhere else for that matter, and generally-speaking, our biggest vacations are back home to MI (from IL) to visit family. DS18 attends a community college this year to establish residency in our (old) home state before he goes on to the University he wants to attend because I don't have $20K to spend in out-of-state college tuition. We live in a very high cost of living area in IL, and my kids go to school with kids who live multi-million dollar homes while we live in a 1300 sq foot brick cape cod that is so close to the house next door to us that I can touch both houses when I stand on my side porch, and the kitchen is 10x6. Many of our family members live in 4000 sq foot houses in MI, and my kids are insanely jealous.
But you know what? When kids come to my house, they may not have their own suite of rooms, or a gourmet kitchen, or a home theater, but they have warmth and care and open arms. And usually some pizza or good snacks lol
DS18's good friend is very well off - lives in a $2M home in a gated community, and guess where he spent most of his senior year? On our couch, talking to DH about football, and his college plans, and his life. This kid's parents traveled a lot for work and were never home. He came to our tiny, old house and didn't care that the dining room table is, for all intent and purposes, in the corner of the living room because we don't have a dining room and there is no way it would fit in the kitchen. He didn't care about our bathroom that needs to be repainted, or the screen door that has a broken handle. He's been to Hawaii, and Mexico, and Europe...New York City, Florida, California...everywhere. But he has said that his favorite trips of all are with DH, DS18, and my BIL 2 hours away in South Bend IN to Notre Dame Footbball Coaching Camps. DH has been taking the boys the past three years. And there have been times when we had barely any money and DH was buying McDonalds for them for dinner and counting quarters for tolls! And this rich kid who "has it all" loves it.
Don't underestimate kids. Not all of them are spoiled rich snotty brats. They honestly do not care about where people live, and if they do, I wouldn't want my kids being friends with them anyway.
I would let your son go on the trip. My kids have been invited on many trips with their friends - DS went to Myrtle Beach with his BFF when they were 14. The friend was from the mom's first marriage, and was pretty much an only child...his little sister and brother were 3 and 2 at the time. The parents just wanted the kid to have someone to hang out with and have fun with someone his own age! DD14 and DS12 have gone on trips with their BFF's too...for some reason my kids are attracted to only children lol, whose parents are always looking for someone for their kids to hang out with on trips. I can guarantee that they are not thinking of it as pity or charity...they are just thinking about how much nicer the teen will be if there is another teen there. I know my own (4) teenagers are MUCH happier, sweeter, and nicer to me when their friends are around...so we invite kids to go with us all the time! haha. And we only offer if we can pay, so it's never a thought in our minds that we are being "put out" by having another kid tagging along.
As for your other kids....they will get opportunities in their lives to do things their siblings don't get to do. That is the last thing I would be worried about. We have 3 kids+guardianship of our great-nephew, and we tell the kids all the time that life isn't always fair or equal in the moment, but equals out over time. If you don't make a big deal over the fairness of one kid going vs the others, they won't either.
Good luck with whatever you decide! You are neither right or wrong either way.