Yes, once you have anchors in the form of vignettes, you can study the reasons for respondents' different understandings. In the chopit model, the thresholds between the response categories are explained with a set of explanatory variables. We can therefore estimate the effects of these variables on the thresholds. Another way to say this is that the model has multiple systematic components, predicting both the actual values of the concept being measured and the actual thresholds between the response categories, across respondents.
Studies such as these are useful in their own right in understanding how respondents see the world and understand the concepts being studied. They can also be of considerable use in designing better survey questions, especially in conjunction with cognitive debriefing sessions.