A number of extensions to the classical notion of functional dependencies have been proposed to express and enforce application semantics. One of these extensions is that of order dependencies (ODs), which express rules involving order. The article entitled "Discovering Order Dependencies through Order Compatibility" by Consonni et al., published in the EDBT conference proceedings in March 2019, investigates the OD discovery problem. They claim to prove that their OD discovery algorithm, OCDDISCOVER, is complete, as well as being significantly more efficient in practice than the state-of-the-art. They further claim that the implementation of the existing FASTOD algorithm (ours)-we shared our code base with the authors-which they benchmark against is flawed, as OCDDISCOVER and FASTOD report different sets of ODs over the same data sets. In this rebuttal, we show that their claim of completeness is, in fact, not true. Built upon their incorrect claim, OCDDISCOVER's pruning rules are overly aggressive, and prune parts of the search space that contain legitimate ODs. This is the reason their approach appears to be "faster" in practice. Finally, we show that Consonni et al. misinterpret our set-based canonical form for ODs, leading to an incorrect claim that our FASTOD implementation has an error.