Well that's the lore, but like a lot of traditions these things come and go, or they change over time. People forget them, or they have their own meanings. I mean diamonds aren't The Marriage Stone because of some deep connection we've had to them throughout human history, for instance. It was just marketing that shifted cultural perception. Things like colored stones and synthetic stones are also very popular now that in the past would have been seen as cheap (and for some people still are), even if the stone itself is actually more rare than a diamond. And then it's going to vary by where you live or what your specific cultural background is, or the way you were raised.

I'm not saying plenty of people don't still reserve the ring finger for marriage, of course. It's just that plenty of them will happily wear a ring there in lieu of an engagement or wedding ring if it fits and is comfortable. I myself can ONLY wear rings on that finger, any other finger gets in the way or is uncomfortable, and it's been that way since I was a kid. Typically it seems like most people won't assume a ring on that finger is an engagement or wedding ring unless it looks very obviously like something intended for that purpose. That's been my experience, anyway.

Though you never know. Sometimes the person who rocks up to the counter with a giant silver owl on that finger IS in fact using it to indicate they're taken.

Anyway I am definitely not arguing one side or the other here, I just think both sides are equally valid because it's such a personal preference thing these days.

edit: Also if this sounds really rushed or some part of it doesn't make sense, about halfway through it became much more important to keep a cat off a roast chicken.