I just don't get the obsession with Mary Sue litmus tests.

Or to be more precise over reliance on them. Why should anyone feel obligated to radically change a character that they and their fellow roleplayers enjoyed just because some test says so. Though if you do manage a 50+ on one of those Mary Sue tests you should do a heavy amount analysis on whether or not you've gone completely around the bend with this character.
That said, if after finding out that your character scored a high Mary Sue score but their Suesh traits are well justified by background and personality and they're still and interesting character, just leave them be. And you don't need a Greek Mythology style fatal flaw to be deep or complex, sometimes that makes you even more of a Sue! To paraphase the great Hector Barbossa of Pirates of the Carribean "And thirdly, these tests are more what you'd call "guidelines" than actual rules." That's how I see Mary Sue litmus tests, guidlines, not strict rules.

I agree that they work much better as loose guidelines rather then strict rules. If your character is meant to go a certain direction, just because they would end up going up or down a few points on a scale doesn't mean one should be discouraged to that direction. As long as it doesn't cause plot holes and it makes sense for the characters then go ahead, let something special happen, pull out that trope that you've been wanting to use but have been too scared to use(unless it's Narm because seriously) but have really wanted to do.

I admittedly haven't really seen anyone obsess over the tests on this site though...

I just did it to see what it said. I was never actually going to change my characters unless a) I felt like they were Mary-sues or b) My character(s) were so bad that no one read the story or they bashed them continueously. I just found the test fun to do.

Well, even on the page where you do it, they tell you pretty much that these are guidelines, and that there are circumstances where these things are acceptable, and most of all that just because they may appear there doesn't make these things bad. Just because it's been done before (and often, I suppose) doesn't mean it can't be done again.