Thanks for the responses, everyone. It seems like people are pretty split.
I keep noticing that some people say "my spot" which is understandable but incorrect in my opinion. By the letter of the law, no individual owns the land. So, it can't be one individual's spot. It's everybody's spot. However, I understand that people get possessive over land that they don't own. We have a long track record of human behavior as evidence.
I think that it's first some first serve, but I'm willing to cede the spot if somebody comes in super pissed off. Personally, I don't care too much that the camp exists in an area where established sites are illegal.
To be clear, this camp is WAY off trail and one drainage away from being one of the most remote spots in the area. It's also a very tidy camp. So, I'm thinking that 1 or 2 groups uses it consistently. I wouldn't use their items. I would just pitch my tent. I realize that staying there is a risk, but it's a risk I'm willing to take because I think it's a small percentage of people who resort to violence without a conversation. I think that I'd be able to de-escalate a tense situation with my words.