Recently, a human evaluation study of Referring Expression Generation (REG) models had an unexpected conclusion: on \textsc{webnlg}, Referring Expressions (REs) generated by the state-of-the-art neural models were not only indistinguishable from the REs in \textsc{webnlg} but also from the REs generated by a simple rule-based system. Here, we argue that this limitation could stem from the use of a purely ratings-based human evaluation (which is a common practice in Natural Language Generation). To investigate these issues, we propose an intrinsic task-based evaluation for REG models, in which, in addition to rating the quality of REs, participants were asked to accomplish two meta-level tasks. One of these tasks concerns the referential success of each RE; the other task asks participants to suggest a better alternative for each RE. The outcomes suggest that, in comparison to previous evaluations, the new evaluation protocol assesses the performance of each REG model more comprehensively and makes the participants' ratings more reliable and discriminable.