I can see both sides of it. In the example given in the OP, I think it does seem a little petty of Sue and Sally to try and prevent Mary from using a term they've repeatedly used in her presence, and explained to her. I would expect that by using it repeatedly in front of her, they were perfectly okay with her knowing about it, asking about it, and finally using it herself--like they were (subconsciously, perhaps) giving her a way to become more part of their group.
But, I also think buvezdevin has a good point about the nicknames, which IMO fall into the same general type of situation. They are more personal, as CluelessBride says, and therefore it's all the more jarring if Outsider overhears John being called "Jackie" once, by his mother, and then immediately starts calling John "Jackie" himself.
When an outsider jumps on an inside term after hearing it only once or twice, especially if it wasn't even said in conversation with Outsider but rather just within their hearing, I think that can be very awkward, and gives off that "trying too hard" vibe. I'm not sure I could really call it "rude" though...
I think you can ask someone to stop calling you by a certain nickname--"Actually, only my mom calls me Jackie, I would appreciate it if you just called me John"--but with something more like a slang term, I think once it's out there, you can't really call it back. As TootsNYC suggests, if you stop using the term for a while, it will probably lose its "value" to the outsider, and they'll stop using it, too; but now, knowing the outsider's tendency to pick up on these things, I think you have to be careful not to mention anything else you don't want them using.
But, in the Sally-Sue-Mary example, it seems like the term had been used often, and in conversation with Mary, and I think it would be rude for Sally and Sue to claim that it's now proprietary. If Mary just overheard them using it once, deduced a rough meaning from context, and then suddenly sprang it on them in their next conversation, that would be weird and awkward, and trying too hard.