Some interesting thoughts! First, even "back in the day," not everything found in a media account was always, shall we say, without possible "embellishment"? However, taken at face value, it sounds reasonable that the Toler ring episode did possibly happen. To find that a ring he had been told was jade was actually agate is interesting. Agate is a type of gemstone. The agate marbles you note were so-called, I imagine, because their coloration shared a resemblance.
Now, Toler, or the media, possibly sought an interesting connection between the two onscreen detectives. Warner Oland did consistently wear what appears to be a jade ring. This can be seen in many of the images we have available in our Gallery here at this site (take a look at a number of images from "Charlie Chan at the Race Track"). It appears, from grainy closeups I have looked at, that Oland's ring carries a carved Buddha image.