Heh, I have strong view on this. YMMV (your milage may vary, take me with a grain of salt) Also, I don't mean to sound as agressive as I might.
Cummon, if that isn't premise for a Mary Sue, please tell me what is.
Because the definition of a Mary Sue tends to be a laundry list of "don'ts" and usually disregards the fact that a talented writer in original fiction can take that rule list of don'ts, break every single one of them, and carry it off so the reader thinks it's a great story.
See Jim Butcher - I believe it's mentioned elsewhere that a talking head is a no-no in writing, and what does Jim do? He gives us Bob. Who is a talking head, literally. He also took the premise of Pokemon--catching funny little spirits and training them up to do your bidding, which was a premise or plot someone else pooh-poohed on--and turned it into Codex Alera.
(They can also break every rule and come out with a poor character, too, which sounds like what happened in your example, but it depends on the author's skill, not the laundry list. You can have a character that's perfectly normal...and perfectly boring. That's bad characterization too. I guess we could call that one a Sleepy Boo?
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Besides, that's an extreme example. Mary Sue can be used to describe any female character who is too strong and not complex enough to counter balence.
In my eyes, that's called poor characterization, period. I don't like it being called Mary Sue because of the Mary Sue laundry list; you start down the road where any strong female is called Mary Sue, warrented or not, and it pretty much nixes the Hero category of characters, because the classical Hero (say, Superman) has a lot of the "traits" of Mary Sue. You start down the road where any hero character is a Mary Sue. And that's not true--see Starbuck, as you mentioned.
Really, the part about "Mary Sue" that really gets me is the laundry list that's connected to it. There's quizzes about it, even. So I don't use Mary Sue when I mean "poor characterization" because I don't believe the laundry list has anything to do with the reason the character is truly poorly made, the reason has to do with the skill of the author, and I don't want to give people the impression that I do think the laundry list factors into it.
And why would a fanfiction character with similar qualities to someone like Starbuck for instance be dubbed a Mary Sue when Starbuck wouldn't.
The reason I actually left BSG fandom was because fans were calling Starbuck a Mary Sue. Seriously.
But the reason a Starbuck-like character in fanfic might be a Mary Sue--she would violate existing facts about the world she's put into. Basically the world would bend, just for her. For example, lets put a Starbuck-like character into a Harry Potter fanfic. Starbuck has a special relationship with Admiral Adama--so naturally, in the HP fic a character like her would have a special relationship with Albus Dumbledore. Starbuck is a crack fighter pilot, and used to do sports--so lets make her a crack Quiddich player. She had a bitch of a mother, and I think a better relationship with her dad, so lets make her mother Slytherin, and her father Gryffindor.
So this hot-shot quidditch star that's a favorite of Dumbledore pops up at Hogwarts, and has a foot in each rival House. She appears out of nowhere. Maybe she replaces Hooch. Half the male cast wants her (Lee/Anders/Baltar/Zak all sleep with her...we can make that Sirius/Lupin/Snape/Some other wizard...). And she has an adventure. Stealing the raider/stealing the flying car a la Harry Potter...
Ewwww. For me, this sort of thing sort of violates the space/time of the HP universe, by making all these major changes, with no canon to back it up, even if it was written well. It's fine in the BSG universe, because that's where she belongs, and she has a long history of connections with other characters that we've seen. She IS a hero of the BSG universe. It's when you drop it into another universe that it starts to really warp the fabric of the universe, because it disregards known rules put into place by the original author of the universe. She's NOT a hero of the HP universe, and the reader knows it.
But it's easier to say "Another character with purple eyes!" then "This character violates the rules of this world." "Uh, what are the rules?" "Well, they're tacit...hard to explain" "You mean there are no rules." "There are, I just can't articulate them! Oh, frak it...she has purple eyes. She's a Mary Sue."
But yeah...my highly opinionated opinion.
Again, I'm mostly against the laundry list part of the definition of "Mary Sue". It's so popular, and so easy to run down and check off when you compare a character to it that any moron can use it to bash a character. See my Starbuck comment above!
