Well, which chain is the fork? Who's rules are you using as the arbiter? What kind of node you run and what it outputs has a direct effect on what is perceived

Well, which chain is the fork? Who's rules are you using as the arbiter? What kind of node you run and what it outputs has a direct effect on what is perceived as being "Bitcoin", as opposed to "a fork of Bitcoin". Humans are the final arbiter of which one is the fork, whether it's by the nodes they run or by the code they decide to merge into the core repo (sometimes after much very political deliberation).