Looking at their list experiment, I think the results could also come from the design (cf my first comment). I am convinced this is a great method to elicit sensitive behaviours but that of course it requires to be well designed otherwise participants could become suspicious about this task. Also I would not use a list experiment to elicit HIV status, we have used subjective expectations in a survey among sex workers to elicit this info and comparing it to biological markers, it performed pretty well as far as sensitivity was concerned but specificity was not great. Indeed the main issue we had is that a few participants thought they were infected while they were not according to their last HIV test and of course the LR will not help with this. Also I anticipate that revealing HIV status can be such a big deal that I am not sure that the LR could work for that.