Chaotic alignment

You know I said last time that nobody ever talks about "4-ply" meaning two different things on opposite sides of the Atlantic? Well, this time I've got something even more fundamental to do with knitting that nobody ever talks about, and it's this.
How the dickens are you supposed to knit so that all your knit stitches line up in such a way that you would naturally knit into the front of them in order for them not to twist? (I am talking about flat knitting here specifically. In the round, it just happens naturally.)
Yet that assumption is ubiquitous. If a pattern calls for a twisted knit stitch, they tell you to knit through the back of the loop. And everywhere, it's just assumed that you always knit into the front of your stitch and that somehow won't twist it. Which means that I am clearly knitting differently from everyone else, but I have no idea how; all I know is that I get just as good results with my technique as everyone else does, as long as I make certain allowances. For instance, if I need to do a raglan decrease at the end of a row and the pattern says "k2tog" (as they generally do on such an occasion), then I need to pick up those two stitches, physically turn them round, and then knit them together from the front. Knitting two stitches together in my normal fashion results in something identical to a sl 1, k1, psso decrease.
The thing is - and we're still talking about flat knitting here, but I'll get on to knitting in the round in a little while - if you look from above the needle, my knit stitches look like this: ///// So it's natural to knit them through the back, as otherwise they'll twist. Contrariwise, as either Tweedledum or Tweedledee was fond of saying, my purls look like this: \\\\\ So you purl through the front. But, hang on! Everyone purls through the front of their stitches, and yet most people apparently end up with a knit stitch on the other side that's purl-way round, so they knit through the front of that. And I don't understand it. I don't see how my purls are in any way different from anyone else's.
I'm therefore assuming that, for most people, all their stitches are \\\\\ on the needle, so you need to look to tell one from the other, which must be quite inconvenient. The way I knit, it's so easy to tell knits from purls even when they're all pushed quite tightly together that I can do it without even looking. If you look at the feature photograph you can sort of see what I mean; it's not quite so easy to see looking sideways like this, but what you can see is that the needle does naturally go into the back of the stitch and not the front. Here's the same piece, but I'm working a purl:

OK, so that's flat knitting. But then you get into knitting in the round, which I've just been doing for my tension swatch for the new sock yarn (having learnt the hard way that flat swatches don't work for anything knitted in the round, because for no reason I can fathom my tension in the round is significantly tighter). And now, because you're not turning the needle round, all the stitches end up aligned the other way, so now the knits are \\\\\ and you knit into the front or else they'll twist, and the purls are ///// and that... is a complete pain in the patootie, as you will see very shortly. Observe:

Fine. All of a sudden I'm knitting the conventional way, which makes me wonder what other people do when they're knitting in the round. But then I look at the instructions for Judy's Magic Cast-On, which is specifically designed for toe-up socks worked in the round. If you do this cast-on, you end up with two interlinked sets of stitches on the two ends of your circular needle (or your DPNs or whatever you're using); you then knit the stitches off the first end, magic-loop back, and knit the other set of stitches, but at this point she warns you that this set of stitches is "twisted" and to untwist them you have to knit through the back. (Um, no, they look normal to me; it's the other set of stitches that appear twisted to me and I have to knit through the front to untwist them.) And then she says after that you just carry on as normal, so I deduce from this that actually everyone (other than me) knits through the front of their stitches both on the flat and in the round, because after this one blessedly normal set of stitches I have to knit through the front for the rest of the sock. I have not the faintest idea how that works. It's obvious to me that if you don't turn the needle the stitch ought to be the other way round from normal. What am I missing here?
And then we come to purling in the round. Oh, great Scott.


And this is why knitting in the round is so slow. I have to pick up and turn Every. Single. Dratted. Purl. You can just imagine the fun I have on cables, especially when I have knit and purl stitches crossing one another; to be honest I also tend to turn knit stitches in cables if I'm doing them in the round, especially if they're going to the back of the cable, because it just makes them that little bit less fiddly to do. I mean, I've got to pick them up anyway, so I may as well.
I'm foxed. Totally flummoxed. Every time I logically deduce that "oh, well, it works this way for me and other people do it like that, so it must work in such-and-such a way for them which is different," I find it actually doesn't. Don't get me wrong; I'm not complaining. The advantage of having my knit and purl stitches slanted in opposite directions outweighs the minor disadvantages of having to do a custom manoeuvre on half my raglan decreases (I don't much like raglans anyway) and the tedium of purling in the round (again, I don't do that much knitting in the round, other than the socks and my famous cable hat). I'm not planning to re-learn to knit just so I can do it exactly the same way as everyone else.
I'd still love to know exactly what I'm doing that's causing the difference, though!