If there was a comma between "a thrown disc, or (a) mini marker disc" like you wrote out, I might agree with you, however that is not how the rule is written. "A thrown disc or mini marker disc" as written in the rule and definition are the same exact thing which = indicate the lie as markers....
So if you find someone's lost or OB disc, then you are not allowed to retrieve it without their approval and should receive a 2 stroke penalty?
Yes it is particularly applicable in that situation, and there are other situations as well.
Now you are adding words to the rule that are simply not there. And what if it was her own disc? Sorry ladies you all get 2 stroke penalty for not marking his own disc, unless you are a tranny maybe. Nowhere in the rule book does it state that only you can mark your own lie. There are situations like the one in the OP that would authorize you(group) to mark another player's disc.