Quick thought experiment:
You run precision, linearity and specificity using a fictional 100 % pure specimen of your target analyte as a standard, either in clean solutions ("standards") or spiked into matrix. Then you repeat the excercise with 10% of an impurity that is invisible to chromatograph detectors (e.g. water) in your otherwise pure specimen, in other words with a 90% purity for your standard. Precision will remain the same, linearity will remain the same (although the line will be shifted downwards by 10%) and specificity will remain the same. BUT, there will be a 10% bias, in other words a 10% inaccuracy unless you know, and correct for, the purity of the standard. In this scenario you cannot infer accuracy from linearity, precision and specificity alone, you also have to know the purity of whatever you use to calibrate, AND whatever you use to spike the matrix. As Bruce points out; "well characterized reference materials, with documented purity etc"
A certified reference material (whether it be a high purity single compound or a sample in matrix) will have been characterised by a battery of independent techniques such as Karl Fischer for moisture, elemental analysis, insolubles, wet chemistry, NMR etc as well as chromatography. Many of these are primary methods - they do not need a standard of the substance being determined. The primary method most familiar to chemists is weighing; the "standard" is a chunk of metal.
Chromatography does not measure anything, it just separates things so that they can be measured by detectors. Depending on the detector, its response per unit quantity is not the same for all compounds, therefore it has to be calibrated using the target analyte, hence the need to have the purity of reference materials determined by methods that do not use chromatography detectors (or at least not the same detector as would be used in the method being validated). A very few detectors (FID for e.g.) are uniform enough in their responses to different compounds that their response to known quantities of one compound can be used to calibrate their responses to another compound. A drawback with this approach is that such detectors are non-selective, so for trace analytes in complex samples it may not be possible to separate the signal for the analyte from interferences. As far as I know the only analytical method that exploits both selectivity and uniformity of response is isotope dilution mass spectrometry.
Peter