I Think that Courtney is aware of alot of thing posted about them and Shayne, and because of this they do things to fan speculation or mess with the fandom in an innocent way.
They removed all of their rings for the Shayne specific video where every other video she is wearing Multiple rings including one on the Traditional Engagment/wedding finger, just found that interesting.
That being said the Ring on that finger is also a plain silver band in the TNTL trivial pursuit so I have a few thoughts,
They just like to wear rings and put one there without thinking (This is my prevailing theory, sorry to Dissapoint.)
They purposfully put a ring on that finger to mess with the fandom (this fits with my mind games theory)
Shayne proposed with this ring on purpose as to not draw speculation that it's an engagement ring (knowing how well Shayne can assess those around him I could see him doing something like this)
Courtney made the choice to only where a simple band as an engagement ring again to not draw speculation that, that's what it is.
I haven't paid too much attention in other videos where you can see the rings to see whether or not Courtney switches what they wear on that particular Finger.
(UPDATE) watching the, Can we guess reddit's favourite frozen dinners on Pit and there is a clearer picture of the ring 28:15, not sure if it's the same one as in the TNTL Trivial pursuit. But it clearly has some kind of rock in it.