Velxir:
The only real answer here is that this is a murky area by strict RAW and you may experience table variance in PFS.
Disclaimer 1: Common sense has no place in a debate about RAW, and please remember Pathfinder (particularly combat) is a rules heavy game, not a simulation. My chess knight can't move in straight lines just because a real knight can.
Disclaimer 2: I have searched high and low for any official (JB, SKR, Mike in the case of PFS) stance on this but can't find one. If anyone can post such a thing please do.
The crux of the matter is whether "invisible" is a specific condition or whether can't be seen by an opponent == invisible. This is important because there is no entry that states that the attacker having Total Concealment or being Stealthed/"hidden" causes the defender to lose dexterity bonus to AC, only that the attacker being invisible does.
http://paizo.com/prd/glossary.html#invisible
Invisible: Invisible creatures are visually undetectable. An invisible creature gains a +2 bonus on attack rolls against sighted opponents, and ignores its opponents' Dexterity bonuses to AC (if any). See Invisibility, under Special Abilities.
To me, that sounds like a specific condition, especially given the last sentence. Please note it says "Invisible creatures are visually undetectable" and not "visually undetectable creatures are invisible". "All Kings are male" does not imply "All males are kings".
The table in the Combat Modifiers table in the CRB specifically uses the term invisible again.
http://paizo.com/prd/combat.html
I do not have the power to become invisible. Just because you can't see me at the moment (due to being in a different place) does not make me invisible. I am simply not visible to you.
If "opponent not able to see me" != "I am invisible", then neither Stealth nor Total Concealment allow sneak attacks.
That said, I would generally house rule the other way, but I personally believe that that <i>is</i> a house rule.
The Blind Fight example above does nothing to counter this. It means exactly what it says against opponents with the invisible condition, which can only be obtained through magic or a special ability that grants it.
However, there is one piece evidence that comes up for the "you can't see me = I'm invisible" camp:
"Blindsense (Ex) Using nonvisual senses, such as acute smell or hearing, a creature with blindsense notices things it cannot see. The creature usually does not need to make Perception checks to pinpoint the location of a creature within range of its blindsense ability, provided that it has line of effect to that creature. Any opponent the creature cannot see still has total concealment against the creature with blindsense, and the creature still has the normal miss chance when attacking foes that have concealment. Visibility still affects the movement of a creature with blindsense. A creature with blindsense is still denied its Dexterity bonus to Armor Class against attacks from creatures it cannot see."
The last line, particularly the "still" could very reasonably be interpreted as meaning that the general rule is that creatures lose their dexterity bonus to AC whenever they can't see the attacker.
As said, murky.
Now, the interpretation that Total Concealment != invisible can lead to some odd situations. The classic example being that a defender with no means of seeing in darkness attacked in a dark room by two opponents with dark vision. If one of the attackers has greater invisibility, he will get to sneak attack and the other one won't. Yes, this is a bit silly. Does the fact that silly situations can arise from a rule mean it is no longer the rule? No. Does it mean the rule should be changed? Maybe.
There is also the argument that if Stealth doesn't allow sneak attack (the only way it can be argued that it does is by going back through the "invisible" rule), then Stealth does nothing and this proves that "opponent can't see me == I'm invisible". This is clearly not true. Stealth let's you sneak past opponents out of combat and hide/reposition in combat. It also lets you gain a surprise round at the start of combat during which you DO get to sneak attack. That's a considerably more powerful skill than, say, Appraise. Most skills don't have a major combat application.
I think an errata is badly needed one way or the other as this is a question that seems to generate some quite heated and repetitive arguments amongst the player base. I really don't care which way the decision comes down, it just needs to be made. In 3.5 an official errata was made that Total Concealment does allow sneak attack. I would be fine with the same thing in Pathfinder, but it hasn't happened.
I doubt, however, we will get an errata. There was the abortive play test of revised stealth rules a couple years back (showing the devs are aware of the issue), but other than that the devs seem to have refused to touch the issue with a ten foot pole. I can't say I blame them as some people are going to be annoyed whichever way they decide, but I would be really pleased if they would just call it.