Interestingly, this has changed over the various versions. In v1 on arXiv, this statement is presented without proof (as Example 2.2). In v3, it is Example 3.3 and has received an extra sentence with a proof hint. In v5 (and still in v7 which is current) it has turned into a Proposition. So it seems likely to me that reviewers complained that there wasn't a proof in previous versions.