But that's the thing with refluffing; what is that line? Where does it begin our end?
Slippery slope arguments aren't particularly valid. As I said before, I'm nearly positive that you've altered, or are playing in a game that has altered, something of the basic conceits presenting in the PHB. It may be something simple, as defining races from a different place, or applying a different appearance to something, but everyone does it. Unless you're 100% pure, your argument above applies equally well to you.
Which is why it's not an argument I'm particularly concerned about. Especially since the answer is 'wherever a group wants to draw the line.' We all draw that line, we just differ about where.
I vaguely remember a debate in the early 3e/4e edition wars where someone was complaining about unlimited magic missile cantrips. I don't remember if they were complaining that 4e wizards got unlimited mms, or if 3e wizards didn't, but the solution proposed was "refluff the mm as a crossbow bolt" or "refluff the crossbow as magical zaps" (this was pre-errata, where mm had a to-hit roll).
Now, that might sound like a solution to someone, but all I saw were corner cases: DR, SR, Resistances, interaction with incorporeal, anti-magic, etc, etc. A wizard shooting mm pretending to be a crossbow (or vice versa) absolutely destroys whatever meaning those words have. I similarly face-palmed when 3e's dmg2 suggested using other races but refluffing them human in campaigns without demihumans (a lot of humans can see in the dark, apparently).
Humans are human. Dwarves are dwarves. Crossbows are not spells, a magic missile is not a crossbow bolt. Greatswords are not shortswords, chainmail is not leather, and fighters are not rogues.
I'm already playing pretend. I will not pretend my pretend thing is something else.
See, my line is 'I don't change how things work mechanically on a refluff.' All of your examples (except the last, fighters/rogues) are exactly that -- altering mechanics to match a fiction refluff. That's where my line is for refluffs. If you cross it, then I may still consider the change, but it's going to be at a higher level of scrutiny that refluffing the fiction behind a class.
As for fighters are not rogues, it turns out that a fighter can actually do most of the things that are 'roguish' about rogues -- climbing, stealing, picking locks, sneaking, etc. -- with the right selection of skills and tools. The only difference then is mechanics like sneak attack or second wind. Different, yes, but not very. I'd have no problem with a fighter that had stealth and proficiency in thieves' tools claiming that he's a rogue, just like I'd have no problem with a rogue with weapon mastery and armor feats that fights in the front line claiming he's a fighter. Yes, one will mechanically be better at the different roles than the other, but I don't limit roles based on optimizations.
And, further, this isn't to say that for the vast majority of the cases, classes in my game work the way they do in your game. Most characters identify roles directly associated with the assumed roles of their class. Some don't, and I provide that leeway in description if the players want it. Frex, the character that started this whole discussion (at my table and here) is a knowledge domain cleric who identifies as a field archaeologist and acts much more like Indiana Jones than anything else. His devotion to his god is backgroundish to him, just something he does, and isn't the central feature of his daily life. Granted, the central feature of his daily life is the uncovering of lost knowledge, which is also the central tenant of his god, but that's how he rationalizes his clerical abilities -- so long as he keeps at it, he'll retain the favor of his god. He doesn't dress in clerical dress, his display of his holy symbol is on the order of many sages that are lay followers of his faith, and he doesn't openly praise his god at all times. Some of his faith do this, but he chooses to be a follower of action, which clearly sets him apart from most of his faith. So, when people ask him if he's a cleric (actually, clerics and priests in my world are titles, and mostly held by non-casting devotees of the faiths) he says no, because to him and others, that would imply a position in the church hierarchy. But his class is cleric.
None of that changes any of the mechanics of the class or game, it just changes the fiction behind the character.