I agree- but I'm trying to understand something a wee bit different. This goes to the idea of why "D&D" (however defined) is, and has remained, a "Big Tent" game.
Okay, I think "What makes it a Big Tent game?", and "What makes it what is is?", are actually two very different questions.
If you want to use your analogy, it wouldn't be that we both saw a western film; it would be "What makes something a western such that people can discuss Stagecoach, The Good the Bad and the Ugly, Unforgiven, Serenity, and Moon Zero Two as westerns? If I wanted to make a western, except it was set in the 70s in Manchester England, what would that look like?"
This is easy - it is basically, "What defines a genre?" I am now pedantic for those who have not considered the definition of genres before.
The interesting thing about genres are that, despite folks trying to make it otherwise, they are defined by inclusion, rather than exclusion. There's some list of tropes. If you have enough of those tropes, you wind up recognized as in-genre by the audience. Lacking a few tropes is fine. Including tropes from another genre is fine. So long as you've drawn enough from the "Bag O' Westerns", you'll be seen as a Western, whether you like it or not.
This is how you cna get a thing like Firefly which has drawn heavily from both the Western and Sci-fi bags, so it is a sci-fi/Western both, recognizably.
Now, I'm writing this talking about fiction tropes, because that's the easiest example to reach for when discussing genre definition. RPG genres will have tropes that aren't about the fictional genre, but are about rules, or playstyle, and the like as well.
The question of why it is a Big Tent game is not so much about precisely what is in the bag, so much as it is about how accessible and flexible those items are, in general.