The basic process of measurement involves comparing an object under study with some standard. Without the standard, we have no (valid or meaningful) measurement. Anchoring vignettes provide one possible standard, or anchor, to make measurements meaningful. They serve the same purpose as medical tests or other physical measurements when they are available. If you can afford to do the physical tests, and if they are accurate in the area which you are measuring, then you have no need for vignettes as anchors.
For some concepts, direct physical measurement is infeasible. Consider political freedom, for example, where a direct test would involve something absurd like handing respondents a sign denouncing the government, sending them out to the town square, and seeing what happened. Similarly, measuring pain is difficult with direct tests, and measuring many aspects of health system responsiveness directly would also be infeasible. WHO has had great difficulty with medical tests in some areas, in part because the people who administer surveys are good at collecting attitudinal data, and not necessarily good at conducting even simple medical tests in diverse settings. And sending medical personnel to the field can be too expensive, especially on a large scale.
For some dimensions of health, using vignettes to anchor self-assessments may generate less measurement error than using medical or other physical tests. For other dimensions, even if medical tests have less error, they have more error per unit cost of administration. For still others, self-assessments corrected by anchoring vignettes can provide a better inexpensive measurement tool than self-assessments alone. And in other areas, medical tests may be more accurate when they are possible to administer, but noncompliance -- when, for example, respondents are asked to bear pain, such as for blood tests, or embarrassment, such as for stool samples or physical examinations, all with more potential benefit to the investigator than the respondent -- can be a worse problem than for survey-based measures; although only one component of bias, noncompliance can sometimes take a more accurate medical test and leave its practical application more biased than a survey measure.