Hi Roland,
Alright, let's do an example:
Full frame, Noctilux (f1), wide open, 1m focus distance, 39 degrees FOV. Focus in the center first, then deflect into a "1/3rd" composition, meaning rotate by 39/6 = 6.5 degrees. Assuming the Noctilux has a flat focus plane (which it doesn't, it's curved in your favor), the focus error is 100cm * (1 - cos(6.5)) = 0.64cm. The Noctilux has 2cm DOF in this scenario which well covers the error.
With a longer lens, the angle goes down, with a wider lens, the DOF increases, either reducing the impact of recomposing on focus accuracy.
Of course the main reason that this seems so harmless is that you are limiting yourself to the center third. As soon as your subject is outside the center third, the effect becomes a lot more prominent, due to the mathematical properties of the cosine..
As a counterpoint to your case, let's assume the opposite extreme of an object at the edge of the frame. To make up for this, instead of the Noctilux let's consider a rather conservative wideangle, a 24/f2.8, wide open at f/2.8, 1m focus distance, 75 degrees FOV. Focus in the center first, then deflect to the edge of the frame. Rotate by 37,5 degrees. Assuming your lens has a flat focus plane, the focus error is 100cm * (1 - cos(37,5°)) = 21 cm. The 24/2.8 lens has 24cm DOF in this scenario, 8cm of which are in front of the focus point and 16cm to the back, so you're well outside your DOF zone and your object will be out of focus. And this is not a particularly fast wideangle.
Take a 21/f4 in the same situation. The focus error is 24cm now, the lens has 31cm DOF (
EDIT: no, actually it has 46), so wide open we're still out of focus (
EDIT: no, actually barely in focus, but with no rear DOF tolerance left) at the edge of the frame, in spite of the rather slow lens.
Also, the effect is completely independent of distance. This is rather obvious mathematically, too. In the 24/f2.8 example, if instead of 1m focus distance you take 100m, you're still outside focus; the focus error is 21m now, the lens has 24m DOF, 8m to the front and 16m to the back. In fact this is a much more difficult case, because you can't just shift to the side for focusing instead of tilting your head.
It's really only a function of the focal length, the aperture, and most importantly the deflection between the optical axis and the object. If you shoot wideangles, as soon as your object is near the edge of the frame, you have a problem, even if your lens is slow.