Am I interpreting correctly that it's not that the derivatives are wrong, but that the values of the inputs might not be what authors anticipate? If that's the case I wouldn't want to change derivatives, but it might make sense to add a note to centroid sampling that calls out the situation in some way.

That's my understanding of Vulkan, yes. I would be surprised if OpenGL is ever actually worse than that in practice, even if the spec allows that (or used to allow it - I didn't dig up the current OpenGL spec text).

This sounds like a note in the spec is sufficient?

Yeah it's probably useful to as an example call out that "because centroids are not necessarily one pixel width apart, derivative functions might not have the values you expect".

MSL and Vulkan wording is simliar to what exists in WGSL:

MSL: (5.4 sampling and interpolation attributes)

If a centroid attribute variant is specified (centroid_perspective and
centroid_no_perspective), the interpolation point sampled needs to be within both the
primitive and the centroid of the pixel.

Vulkan: 9.12 interpolation decorations (the normative above the paragraph Kai quoted):

If the Centroid decoration is used, the interpolation position used for the variable must also fall within the bounds of the primitive being rasterized.

WGSL:

centroid: Interpolation is performed at a point that lies within all the samples covered by the fragment within the current primitive. This value is the same for all samples in the primitive.

D3D is more prescriptive about exactly what sample location is chosen, while the others allow a lot more choices, potentially.

But all three have the "you're not likely to get something intuitive" vibe. I'd go with a note at best.