I think itsjustme was specifically referring to resistors right on the integrated circuit, but what was stated, that they "must be semiconductors" is wrong. They can be built from a diffused region where you take advantage of the bulk resistivity of the diffused semiconductor material (but not acting as we think a semiconductor), you can build it in the epitaxial layer, and you can diffuse thin film resistors right onto the chip. The former 2 are not very accurate and tend to be rather temperature sensitive. Thin film on chip is not very accurate unless trimmed and that would typically only be done for op-amps with on chip resistor dividers.
I completely agree with your short path arguments, though you probably need to better define accuracy.