I don't see what any of this has to do with integrity.The entire post is about how unimportant the framework of the setting is e.g. "I'd get out the map and me and my sister and/or my buddies would decide "Well, hey, maybe there's killer kangeroos over here!" I mean so what?"
I'm sure that's the definition of setting integrity that @Micah Sweet was using (he can correct me if I'm wrong) i.e. the game world has parameters/rules. @AbdulAlhazred 's post was basically saying, hey, don't worry about those rules, just have fun! Which is a perfectly acceptable way to play. Other tables aren't down with that.
I mean, presumably there are rules that describe the earth (our actual human homeland) but some of them are not known, some perhaps are unknowable, and most people know none of them and even the greatest scholars know only a handful of them each.
So if someone uses parameters/rules to decide what to include in a setting, well good luck to them, but equally they might do what REH did - which is just pinch stuff from the real world and overlay a bit of fantasy fiction - and the setting may well be just as realistic (taking the earth as an example of something realistic because real) and have just as much integrity.
I mean, in my first session of Torchbearer we decided that there is a Wizard's Tower on the south side of the Bluff Hills, and a Forgotten Temple Complex on the edge of the Theocracy of the Pale just north of the Troll Fens. That was done spontaneously by me and the players, with no reference to rules or parameters other than the general Torchbearer rules for settlements.
In today's session, the PCs met with Lareth the Beautiful, who is the half-brother of one of them. This was put to Lareth, and there was more discussion of the family and family origins of the Elven PCs. There was also information about the Forgotten Temple Complex (which some might call a former Temple of Elemental Evil) relayed to the PCs by Lareth. These various bits of information about the setting have been authored primarily by me, over the past few sessions. The method is not wildly different from @AbdulAlhazred and his sister and friend's method, of what would make for fun play in these circumstances?
I can tell you that the setting of our game has integrity, and you can refer to the actual play linked to above to see the evidence.
And if by "setting integrity" is mean not changing the setting from game to game, that's an odd usage. "Setting continuity" or "setting repetition" would both see more apt.