Privacy-Preserving Record Linkage (PPRL) aims to identify records that refer to the same entity across databases held by different organisations without revealing sensitive information about the entities whose records are being linked. Research has shown that some popular PPRL techniques can be vulnerable to reidentification attacks. In response, the use of Differential Privacy (DP) has been investigated with the aim to provide formal privacy guarantees for PPRL. Multiple studies have explored the use of DP during the blocking stage, where similar records are grouped prior to comparison. Yet, since encodings of individual records must be shared for comparison and classification, the linkage process remains vulnerable to attacks despite being differentially private during the blocking stage, unless a computationally expensive secure multi-party protocol is used. Other studies have explored the use of DP during the encoding stage to guarantee that encoded records remain private even when exchanged between the parties involved in a PPRL protocol. While such approaches do employ established DP methods, we consider that their current application in the context of PPRL is nonsensical. The purpose of PPRL is to identify, with highest possible accuracy, specific records that refer to the same entity, while DP perturbs sensitive data to prevent possible reidentification of individuals within a data set. Therefore, this is a mismatch of paradigms. In its current use, DP for PPRL requires substantial perturbation to guarantee privacy, which in turn leads to a notable degradation of linkage quality. To support this argument, we survey and review the use of DP for PPRL, focusing on its effectiveness in protecting the real-world entities (generally people) whose records are being linked.