Since Dana hit it on the head with the realm of no absolutes / styles point, I'll chime in here with the degree of freedom that's available
As an instructor my opinion is that there are two aspects here: the d-loop alignment and the casting loop alignment.
The proper casting loop
flies beside the rod tip, that is to say:
The bottom half of the loop is in alignment with the rod tip but the upper half flies parallel to the casting side "beside" to use your words.
The wedge or loop leading edge turning over tilts to the outside to join the two vectors and the top half of the loop flies in a parallel plane. If the loop is like a pulley wheel, then we could say that the pulley is tilted slightly to the casting side.
The amount of this tilt and the gap between the two vectors depends on as Dana says, your style and technique.
But a pulley is not comprised of just one wheel, there is another wheel - the D-loop...
is correct if it successfully generates the above casting loop configuration - most commonly the d-loop will be tilted at a complementary angle to the casting loop, which means mirror image from the rod tip to the water (I'll draw up some diagrams). But this is not always the case, and the alignment of the d-loop to the tilted casting plane varies a bit from cast to cast (e.g. a single spey 90 degree change cast vs. a Double Spey).
This has more to do with change of direction practicality than anything else. One can achieve a much more compact alignment of a d-loop with a double spey's intermediate movement than they could with a long belly 90 degree change of direction. However, they are both fine if the generate a proper casting loop, which as noted above can be tilted as a two-wheel pulley can be tilted.
In general we position the anchor on the casting side at approximately a rod's length away from the body, and drive the casting stroke just inside that position as we come forward. Placing the anchor far and stroking close doesn't work well, placing the anchor close and stroking far doesn't either. If you place close, stroke close, if you place far stroke far. This keeps the tilt of the two wheels of the pulley workable. As long as the casting stroke can generate the casting loop from the d-loop things go pretty well hence the variation in styles and techniques as Dana says.
The key is because you can generate enough casting power with a slightly tilted pulley as you can with a vertical pulley, both casts are fine however the nature of setting a d-loop with a change in direction cast like a single spey requires that the caster learn to use a tilted system.
Experiment with this, and I hope the two-wheel pulley metaphor helps you as it's helped me and those I've worked with. Just don't take it too literally