Most people don't have any real idea what those terms actually mean in terms of narrative. Or rather, since there is no 'official' academic standard, people don't have very rigorous definitions for those things. Mary sues more often than not, to them, are just people who happen to be extremely talented, when that is way too broad a definition of the term if you think about it. And I've seen more than one person genuinely try to argue that a mary sue can just be a character they happen to dislike. When you have that weak and flimsy a definition, a mary sue can be anyone regardless of the flaws they have or circumstances surrounding them.
Korra of LoK seasons 1 and 2 is a Mary Sue in that things in the story don't function the way they should, but do so to giver her achievement in the narrative. Elements of this can be even found in season 3. Korra kept the gate open, but it wasn't because of any belief or new insight she had. Her reason began and ended with "Well, why the hell not?" Tenzin and Zaheer and others all believe it was the right decision, but she didn't make it with any motivation or intent that can be read as wise or noble. Yet the characters all praise her for it, when all it was was a whim.
As far as TLA goes, obviously, we all have our biases, but I like to think I am appropriately critical of TLA and LoK. I just genuinely come to the conclusion that LoK really is that inferior and have plenty of reasons I can back that up with.
